FF13. Weapon.

Lightning

Lightning is the best Ravager in the game. While Hope has more spells, and is the only character who can learn every tier 3 elemental spell, Lightning is more versatile. She gains every tier 2 elemental spell, along with Thundaga, as well as every elemental strike, and this makes her useful against both magic-resistant and physical-resistant enemies. Hope cannot boast that level of versatility. Lightning also makes a fantastic Commando, but due to her abilities as a Ravager, it is best to have another character be your primary Commando.

As a result of this, Lightning needs a balanced weapon. Because of this, I'm counting the Gladius out of consideration. The Gladius is a popular weapon for her, and it's a great choice in the early game, when she and Hope are together and Lightning is your only possible Commando. Later on, it's a bad idea to focus too heavily on one statistic for her. Other weapons that are ruled out: Organyx, because it drastically slows down Lightning's attack speed; Lifesaber, because its bonus is nearly useless and doesn't even remotely offset the weapon's weakness; and Hauteclaire, because Lightning is possibly the worst character to have Stagger Lock.

This leaves the Blazefire Saber, the Axis Blade, and the Lionheart.

The Blazefire Saber is a great choice throughout the game, and is most likely the best option until Chapter 12. It allows Lightning to be equally effective as a Ravager, Commando, and Medic.
->Blazefire Saber (Lv. 26, 24,600 EXP to max) + Perovskite
--->Flamberge (Lv. 61, 445,950 EXP to max) + Trapezohedron
----->Omega Weapon (Lv. 100, 1,296,897 EXP to max)

The Axis Blade has very low stats. However, it has the Attack: ATB Charge special property, which is exactly what it sounds like: it will slightly charge your ATB every time you land an attack. This, combined with other speed-boosting accessories, will turn Lightning into an incredibly fast character. In my opinion, however, this is not her best weapon. Nonetheless, I'm including it here because it is a popular choice for her.
->Axis Blade (Lv. 21, 66750 EXP to max) + Adamantite
--->Enkindler (Lv. 41, 280,830 EXP to max) + Trapezohedron
----->Omega Weapon (Lv. 100, 1,419,867 EXP to max)

The Lionheart again has lower stats than the Blazefire Saber, but higher than the Axis Blade. However, this is likely the best choice of weapon for Lightning. This is because of the Quick Stagger ability, which will allow you to stagger an enemy 10% earlier than normal. This is a fairly small boost in staggering speed, but it is noticeable, especially against enemies with high stagger percentages.
->Lionheart (Lv. 21, 63,060 EXP to max) + Scarletite
--->Ultima Weapon (Lv. 41, 221,900 EXP to max) + Trapezohedron
----->Omega Weapon (Lv. 100, 1,482,487 EXP to max)


Sazh

Sazh is likely the best Synergist in the game. He wins over Hope because he learns Haste earlier and because he learns Vigilance. Unfortunately, that's all that Sazh really has going for him. He's a terrible Commando and lacks elemental versatility as a Ravager. Plus, his natural stats are the lowest of any character. Luckily for Sazh, he has the strongest weapons, which help to offset his low stats.

As a result of this, Sazh is best served with a weapon that has high stats. This immediately rules out the following: Vega 42s, Antares Deluxes, and Procyons. Though the last two have interesting special properties, Sazh's stats are low enough that he needs higher stats more than he needs special properties. This leaves us with several options, but I'm going to immediately rule out Aldebarans because of the painfully slow attack speed and complete lack of strength and Pleiades Hi-Powers because they dramatically lower his maximum HP and completely lack magic. This means I'll be discussing the following: Spica Defenders, Deneb Duellers, and Rigels.

The Spica Defenders have the lowest stats of the weapons I'll be discussing. They favor magic over strength, which is fine, because Sazh is a terrible Commando. That said, they have the Augment Maintenance special property, which will increase the duration of Sazh's offensive buffs, such as Enfire, by quite a bit. This makes the Spica Defenders a good choice for a Sazh focused primarily on being a Synergist. Unfortunately, they lack the versatility of the other two choices.
->Spica Defenders (Lv. 21, 66,750 EXP to max) + Scarletite
--->Sirius Sidearms (Lv. 41, 218,210 EXP to max) + Trapezohedron
----->Total Eclipses (Lv. 100, 1,737,313 EXP to max)

The Deneb Duellers are focused entirely on having a high magic bonus. Since Sazh relies on magic more than strength, this is great. They have no special property other than this, but in my opinion, they tie with the Rigels for the best weapon choice for Sazh. (By the way, did anyone else notice the subtle nod to Ogre Battle? While all of his weapons except the Total Eclipses are named after traditional star names, like Balthier's guns from Final Fantasy XII, Deneb and Canopus are also both characters from the Ogre Battle series, of which several developers have joined the Final Fantasy team. I thought it was a nice touch!)
->Deneb Duellers (Lv. 26, 33,000 EXP to max) + Perovskite
--->Canopus AMPs (Lv. 61, 437,550 EXP to max) + Trapezohedron
----->Total Eclipses (Lv. 100, 1,551,723 EXP to max)

The Rigals are your best option if you want a more versatile Sazh. The problem is that they have Stagger Lock, which will prevent Sazh from landing the staggering blow on an enemy. This is fine only if you have another Ravager in the party--if not, the Rigels are a terrible choice. However, if Sazh is not your primary Ravager, I believe that the Rigels tie with the Deneb Duellers as the best weapon choice for Sazh.
->Rigels (Lv. 26, 54,800 EXP to max) + Uraninite
--->Polaris Specials (Lv. 61, 332,560 EXP to max) + Trapezohedron
----->Total Eclipses (Lv. 100, 1,634,913 EXP to max)



Snow

Snow is the best Sentinel in the game due to his incredibly high HP score. Fang is a great Sentinel as well, but she doesn't come anywhere near Snow's sheer endurance. Snow is also a capable, if limited, Ravager, and a fantastic Commando, though he loses out to Fang. This means that Snow tends to require fairly balanced weaponry if you wish to make use of all of his capabilities. Nonetheless, one can be forgiven for focusing on strength for Snow, as he will likely be a Commando and a Sentinel more often than he'll be a Ravager.

As a result, I'm counting out the Feymark, as it makes him a useless Commando, and the Sacrificial Circle, because it will greatly lower his capability as a Sentinel due to dropping his HP. The Umbra is too situational with its Improved Ward special property to be worth the lowered stats, as is the Paladin. Frankly, Snow is survivable enough as it is, and he doesn't need to sacrifice strength and magic to improve that. As a result, I'll be discussing the Wild Bear, the Power Circle, and the Rebel Heart.

The Wild Bear is Snow's version of the Blazefire Saber. It lacks special properties, but it's his most balanced and reliable weapon. As a result, it's a great choice for Snow to keep throughout the game. In fact, Snow can benefit form the Wild Bear more than Lightning can from the Blazefire Saber, most likely.
->Wild Bear (Lv. 26, 24,600 EXP to max) + Perovskite
--->Feral Pride (Lv. 61, 445,950 EXP to max) + Trapezohedron
----->Save the Queen (Lv. 100, 1,246,803 EXP to max)

The Power Circle is a weapon focused on raw strength. This is a great weapon for a Commando or Sentinel Snow, but it will limit him as a Ravager to being most effective with elemental strikes. Nonetheless, I believe that the Power Circle ties with the Wild Bear as the best reliable weapon for Snow.
->Power Circle (Lv. 26, 89,700 EXP to max) + Scarletite
--->Battle Standard (Lv. 61, 476,940 EXP to max) + Trapezohedron
----->Save the Queen, (Lv. 100, 1,150,713 EXP to max)

The Rebel Heart is a risk vs. reward weapon. It has the balance of the Wild Bear but lower overall stats; however, it has the Critical: Power Surge ability, which will greatly increase Snow's stats when his HP reaches critical levels. This makes it an interesting choice for Snow. He'll be taking damage often as a Sentinel, and his high HP means that critical HP for Snow is more than critical HP for any other character. It might just be worth it, especially if Snow isn't your party leader, so give it a try for yourself.
->Rebel Heart (Lv. 21, 38,040 EXP to max) + Uraninite
--->Warrior's Emblem (Lv. 41, 153,000 EXP to max) + Trapezohedron
----->Save the Queen (Lv. 100, 1,526,313 EXP to max)


Hope

Hope is the best Medic in the game, winning out over Vanille due to a higher potential magic stat and his superiority in other roles. He is also the second-best Ravager as mentioned in the Lightning section: he is the only character who receives Firaga, Blizzaga, Thundaga, Aeroga, and Waterga all together. This makes him the best magic-based Ravager, but he lacks elemental strikes, which makes him less useful against magic-resistant enemies. He is also the second-best Synergist, losing out to Sazh only because he learns Haste late and cannot learn Vigilance.

As a result, Hope has absolutely no need for strength. That means we can count out any of his weapons that sacrifice anything at all for increased strength; this includes the Airwing and the Simurgh. Hope also has the absolute lowest HP of any character, by quite a bit, which makes the HP sacrifice of the Malphas an unwise trade-off. As he is such a good Ravager, Alicanto is a waste, due to Stagger Lock. Ninurta lacks any distinguishing qualities whatsoever except for balanced stats, and as stated before, Hope doesn't need balance, he needs magic. The Vidofnir looks nice, due to Defense Maintenance, but this pales in comparison to Sazh's Augment Maintenance, as it only affects Protect, Shell, and Veil. This leaves the following:

The Hawkeye is for pure magical power. In my opinion, this is the most important thing for Hope to have, which makes the Hawkeye the best weapon choice for Hope. It lacks special properties, but it's hard to ignore just how much this boosts his already-high magic stat. Its second tier form, the Eagletalon, gives him a whopping 506 magic, and that's only second tier.
->Hawkeye (Lv. 26, 33,000 EXP to max) + Perovskite
--->Eagletalon (Lv. 61, 437,550 EXP to max) + Trapezohedron
----->Nue (Lv. 100, 1,084,542 EXP to max)

The Otshirvani has lower stats than the Hawkeye, but it has a special property: Siphon Boost. This makes the various *siphon abilities in the Ravager tree more effective, allowing him to be an even better Ravager and boost the enemy's chain gauge even faster. I don't personally think it offsets the difference in magic from the Hawkeye, but it remains a great choice.
->Otshirvani (Lv. 21, 66,750 EXP to max) + Scarletite
--->Urubutsin (Lv. 41, 218,210 EXP to max) + Trapezohedron
----->Nue (Lv. 100, 1,270,132 EXP to max)



Vanille

Vanille is the best Saboteur in the game, winning out over Fang due to increased magic and the Death spell. She also makes a fantastic Ravager and Medic, though Hope outshines her in both roles. As a Ravager, she lacks some of Hope's versatility, as the only third tier elemental spells she learns are Firaga and Blizzaga, and as a Medic, she has lower magic, and thus less healing power, than Hope.

Like with Hope, Vanille has no use for strength, so one can immediately count out the Binding Rod, the Tigerclaw (which is also slow due to Leadenstrike/Ironstrike), and the Rod of Thorns. As she will likely spend a lot of time as a Ravager if she is in your group, the Stagger Lock on the Heavenly Axis is unfortunate. Mistilteinn is interesting, as it will increase her strength and magic if an ally is KO'd, but as you'd likely rather avoid a KO, especially if Vanille isn't your party leader, I'm going to leave it out. This leaves the following:

The Pearlwing Staff is Vanille's version of the Hawkeye. If your Vanille is all about magical power, you can't go wrong with this one. However, Vanille, like Lightning, has some of the best special properties to her weapons, so the Pearlwing Staff is less than ideal for Vanille.
->Pearlwing Staff (Lv. 26, 33,000 EXP to max) + Perovskite
--->Brightwing Staff (Lv. 61, 437,550 EXP to max) + Trapezohedron
----->Nirvana (Lv. 100, 1,393,818 EXP to max)

The Healer's Staff makes Vanille the best Medic in the game if you equip it. It has much lower stats than her other weapons, though. Why is it here? It has a very interesting synthesis group: High HP. Combined with the right accessories, it will boost her strength and magic if she has over 90% HP. That means that she can (somewhat) make up for the Healer's Staff's weakness simply by keeping herself healed and wearing the right accessories! Nonetheless, this may lock you into certain accessories, limiting her versatility.
->Healer's Staff (Lv. 21, 63,750 EXP to max) + Adamantite
--->Physician's Staff (Lv. 41, 217,410 EXP to max) + Trapezohedron
----->Nirvana (Lv. 100, 1,583,205 EXP to max)

The Belladonna Wand greatly increases Vanille's chances to successfully debuff an enemy. Combine that with its quite decent magic stats, and the Belladonna Wand shines as the best possible weapon for Vanille. Plus, this weapon's second form, the Malboro Wand, is necessary if you wish to use Death to get the Growth Egg early and farm Adamantoises.
->Belladonna Wand (Lv. 21, 38040 EXP to max) + Uraninite
--->Malboro Wand (Lv. 41, 153,000 EXP to max) + Trapezohedron
----->Nirvana (Lv. 100, 1,673,280 EXP to max)



Fang

Fang is the best Commando in the game, winning out over Snow because of her incredibly high strength and the massive strength bonus she can get from her weapons. Fang is also a very capable Saboteur and the second-best Sentinel, losing to Snow because he has so much more HP than she does. Surprisngly enough, once she has access to her non-innate roles, Fang is a very good Ravager. She gets all of the elemental strikes, as well as Waterga and Aeroga. Simply put, Fang is a fantastic character all around.

As you might expect, this makes choosing a weapon for her difficult. The Bladed Lance is good, but not good enough to keep up with the rest of her weapons. The Partisan is too focused on magic to do justice to Fang's versatility. The Dragoon Lance has a similar problem, though it warrants a little more consideration, as it is an incredible weapon for a melee-fighting Fang; the problem is, its Stifled Magic makes her Ruin and Ruinga spells, as well as her Saboteur spells, much less useful, and so, though this may be an unpopular decision, I'm not counting it in as a candidate for her best weapon. It simply makes her useless against physical-resistant enemies, and there are enough of those that this is a problem. The Shamanic Spear is the opposite of the Dragoon Lance, and is, again, counted out, because it severely weakens her melee capabilities. The Punisher can help save you time building TP, but there are plenty of accessories that can do the same thing, and it isn't really worth it. That leaves these three choices:

The Gae Bolg lacks raw power, but is great for Fang focused on being a Sentinel. Its Improved Counter ability will greatly increase the damage Fang does with her counterattacks in the Sentinel role, and so it can be a very useful weapon, if you're willing to live with the decreased stats. Improved Counter isn't as good or as versatile as Lightning's Quick Stagger, so I don't consider it her best weapon.
->Gae Bolg (Lv. 21, 70,850 EXP to max) + Scarletite
--->Gungnir (Lv. 41, 214,110 EXP to max) + Trapezohedron
----->Kain's Lance (Lv. 100, 1,484,665 EXp to max)

The Pandoran Spear is optimized for Fang as a Saboteur. Its Improved Debilitation will increase the chances of her Debrave, Defaith, and Slow spells being successful, which makes it very nice. It favors magic over strength, but it has almost the same amount of strength as the Gae Bolg, making it a fair choice, though still not the best.
->Pandoran Spear (Lv. 21, 70,850 EXP to max) + Scarletite
--->Calamity Spear (Lv. 41, 236,350 EXP to max) + Trapezohedron
----->Kain's Lance (Lv. 100, 1,462,425 EXP to max)

The Taming Pole has the best overall stats of any of Fang's weapons... but it has Stagger Lock. Remember how I said that Fang is a great Ravager? She's a better Commando, and a Commando really doesn't need to be able to deal the staggering blow. Stagger Lock won't prevent her from increasing the chain gauge, nor will it hinder the Commando's ability to slow the gauge's falling. I never use Fang without another Ravager in the party anyway, so Stagger Lock is forgivable for her; this makes the Taming Pole her best weapon in my eyes.
->Taming Pole (Lv. 26, 54,800 EXP to max) + Uraninite
--->Venus Gospel (Lv. 61, 332,560 EXP to max) + Trapezohedron
----->Kain's Lance (Lv. 100, 1,382,265 EXP to max)