The equipment I used to beat the game:
Rikku:
G-Grid: Black Tabard
D-Sphere: White Mage(with Black Mage mastered)
Other things:
Crystal Ball (Magic +50 I believe)
Crystal Bangle (HP + 100%)
Yuna:
G-Grid: Undying Storm(I think thats what it was called. The plus 15 attack and magic one)
D-Sphere: 100% Gunner
Other things:
Diamond( I think) Gloves(Defense + either 40 or 50 not sure)
Mythril Bangle(HP +60%)
Paine:
G-Grid: Undying Storm
D-Sphere: The all powerful 100% Dark Knight
Other Things:
Mythril Bangle(HP +60%)
Champion Belt(Attack +40 I think)
Well, there ya go. Feel free to chime in other people.
Here’s my general tip: Always make sure to do as much as you can of the Via Infinito before starting New Game Plus. There’s just so much good stuff down there that you don’t want to miss it.