I'm gonna suggest 360. You said you like achievements, so that's a plus, and online play is silky smooth. Join a party with a few friends, and you'll have a blast.
On the subject of the controller, I'd suggest getting either an arcade stick or one of those new FightPads as soon as possible, but I think I should also mention that the controls aren't nearly as difficult to manage with a standard 360 pad as they are in other fighting games. Combinations that usually require extremely precise inputs (like, say, the Dragon Punch motion) can now be done relatively easily with the analog stick, and almost 100% of the time with the d-pad. At least give it a try before you go out and buy something new; you might find it suits your purposes just fine.