For NGS, it is fairly simple: if the weapon icon is Orange (Sword, Partizan, Wired Lance, Daggers, Doublesaber, Knuckles, Katana, Dual Blades), Melee/Striking Weapon Potency/Damage increasing augments are the way to go (ie. Might/Power augments, etc.); for Blue icon weapons (Rifle, Launcher, Bow, TMGs), Precision/Ranged Weapon Potency/Damage; for Yellow icon weapons (Rod, Talis, Wand, Jet Boots, Takt/Harmonizer), Tech Weapon Potency/Damage. From there, I personally can't really help with the nuances, you just have to consider things like Minimum Damage increases, HP or PP, Guard, etc.
Keep in mind that this also applies even when Multi-weaponing, so a Sword/Rifle multi-weapon would need both Melee/Striking and Precision/Ranged.
You might be able to get better advice on augment builds in the Phantasy Star Fleet Discord, considering how dead it is here.
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