The best

I'm going to run through the best champs of each role as my perspective, through gameplay and observation  I have found these champions the best, though they do have downsides.

AP MID - Morgana (AoE, Spellshield, 2 forms of CC, plenty of damage even when playing tanky)
AD CARRY - Vayne (Large AD steroid, Invis, CC (knockback), 2 gap closers, true % damage)
                       Caitlyn, i agree that Vayne is the best, Caitlyn is my favorite though and I will talk about why.
SUPPORT - Taric/Janna couldn't decide (CC, + Steriods, Heals,)
JUNGLE - Lee Sin (steroids, high mobility even without flash, cc, heavy slow, 2 gap closers, good duelist)
TOP - AD Riven (mobility is high, cc, steroids, good duelist, sustained damage, shield)
           AP Rumble (LOTS OF DAMAGE, huge slows[good for 1v1], plenty of sustained damage, shield)