Any item you are looking for that isn't listed below either doesn't exist in the realm of FF8 or is incredibly easy to obtain via refinery.
Adamantine: You'll need these to make some of the best weapons. Go to Long Horn Island near Dollet; you can occasionally fight Adamantoises on the beaches there, and they'll drop Adamantines fairly often.
Aura Stone: Learn Tonberry's Familiar ability. Then buy Power Wrists or Hypno Crowns from the Esthar Pet Shop and use Tool-RF to make them into Aura Stones.
Barrier: Mug Behemoths.
Cactus Thorns: Frequently won from Cactaurs.
Curse Spike: You'll need 100 of these to make a Dark Matter. They can be stolen from Tri-Faces, and occasionally won from Forbiddens, Malboros, Tri-Faces, Imps, Creeps, and Grand Mantises.
Dark Matter: This can be refined into some useful items. Get Siren up to Level 100, then get 100 Curse Spikes and use Tool-RF on them.
Dino Bone: Mug T-Rexaurs to get these.
Dragon Fang: Needed for the Lionheart. Blue Dragons drop them more often than other enemies; you can find them on the Island Closest to Hell and the forests of Trabia.
Dragon Fin: Mug Grendels.
Dragon Skin: Anacondaurs drop them fairly often.
Energy Crystal: You'll be using quite a number of these if you're trying to make everyone's best weapons. Fight the regenerating Elnoyle in Esthar to get all you need.
Fury Fragment: Mug Blue Dragons to get it.
Inferno Fang: Mug Ruby Dragons.
Laser Cannon: Mug high-level Elastoids or the Mobile Type 8 boss.
Lightweights: You can win them from Vysages.
Malboro Tentacle: Defeat or Mug Malboros.
Moon Stone: Mug the regenerating Elnoyle for these.
Power Generator: Occasionally obtained by Mugging high-level Blitzes.
Red Fang: Mug Hexadragons.
Star Fragment: Mug Iron Giants. A number of enemies on the Island Closest to Hell drop them, too.
Whisper: Mug Adamantoises.
Wizard Stones: Buy Magic, GF, Draw, or Item Scrolls from the Timber Pet Shop and use Tool-RF to make them into 10 Wizard Stones each.