Dold text: I can try to break down some of the abilities I know and what weapons I recommend. Late into the game +200 str/mag isn't really that much (you get a bunch of 15+ str/mag crystals as the crystarium grows). Accessories can make up for stats too.
Abilities you don't want:
Paper/Silk Tiger: Reduces your max HP by a big percentage up to ~60%.
Leadenstrike/Ironstrike: Reduces your ATB recharge speed. So Organyx is not Lightning's best weapon. It has the best stats but it'll make you 60% slower.
Stagger Lock: You can't stagger enemies. This one you may or may not want. It's okay with people like Fang or Snow because you're not really going to stagger any enemies with commando attacks. You stagger enemies most likely with magic.
Recommended weapons to upgrade for each char:
-Blazefire Saber: has balanced decent max stats. No abilities. Good until you find another weapon.
-Gladius: has good Str but low magic. No ability. Good for people who use Light in Commando role.
-Lionheart: Her best weapon imo but not available til chapter 12. Balanced str/mag. Quick Stagger ability which will let you stagger enemies at about 85% of the bar.
-Axis Blade: has the worst stats but it makes you recharge your bar quicker. With haste and speed accessories this can be crazy.
-Hauteclaire: has next best stats to Organyx but you can't stagger enemies with Lightning.
-Belladonna Wand: Improved debuffs. Vanille is the best debuffer in the game you can really cripple shit. Every other weapon isn't worth it for her. This weapon makes her one of the best chars imo. It also increases your chance of landing death on enemies (good for farming hard ass enemies).
-Taming Pole: Best stats. You just can't stagger enemies with Fang.
-Pandoran Spear: Decent stats and you dehabilitate better (slow, curse, etc.) I went with this one.
-Vidofnir: Decent mag stat. Makes your buffs last longer.
-Hawkeye: Best mag stat. No ability.
-Wild Bear: Decent stats no ability.
-Rebel Heart: Power up at low health, decent stats.
-Power Circle: Good str, Snow sucks at magic so low magic doesn't matter anyway.
-Procyons: Makes enemies stay staggered longer.
-Spica Defenders: Makes your buffs last longer.