[color=magenta]Well, it has been a little while since I have played FF 3/6, but it is my favorite game of all time. I was considering starting it up again, but when I heard that it was going to be released on the GBA this year, I decided to wait until it is released. So anyways, I am a little bit rusty, but here is some of the stuff that I remember...
The Illumina is pretty much the best weapon around, you get it by transforming Ragnarok into a sword, and then betting it at the Colosseum.
You can turn the Cursed Shield into the powerful Paladin Shield by winning 255 battles while it is equipped. Make sure to equip the Ribbon Relic to cancel out most of the status effects from the Cursed Shield. The Paladin Shield also allows for you to learn Ultima, so if you have Ragnarok turned into a sword instead of being left as Magicite, you will still be able to learn Ultima.
The Snow Muffler can be equipped by Mog and Gau, and you get it by betting the Behemoth Suit (obtained by defeating SirBehemoth) at the Colosseum. It provides a lot of elemental defenses, and it makes the wearer almost immune to regular attacks.
Genji Glove plus Offering relics allow you to attack 8 times per turn, combined with the Quick Spell you can attack 16 times.
Gem Box Relic, (plus the Economizer, which reduces MP cost of all spells to 1 MP apiece, it isn't necessary, but certainly helpful, or even the Gold Hairpin, which cuts MP cost in half.) plus Quick and Ultima spells, it allows you to cast Ultima 5 times in one turn, which can pretty much destroy almost anything in one or two tries.