I'll be looking for tournaments where there are 16 or 32 players and it's RANDOM SELECT. No fighting over who you are using, everyone needs to have a basic knowledge of all fighters to be competitive.

Chess online should be great as well.

Probably Chess and Puzzle, actually. I've fought in Versus quite a bit with other people (yet another reason I want a one player versus mode) and I hardly ever do puzzle/board games with anyone else.

I will be playing the fighting part of MK: D online. I am not very good at chess nor tetris, so I guess I will stick to the fighting part most of the time. When it comes to MK: D the fighting part of the game I will focus at trying to master since day one and on the side might play someone online once in a while in chess or the tetris like game.

i think the chess kombat looks a lot of fun

1.Versus Mode
2.Puzzle Kombat
3.Chess Kombat

First, I'd probably do Versus first, only because I've never played a fighting game online before, but I will probably do Chess the most, It looks like a lot of fun.

Probably Chess, I loved the Wrath unleashed demo, but I never bought it, and the strategy of that Archon style gameplay is excellent, and having a rock-solid fighting engine underneath will make it even better.
Perliminary choices:
Grunt: Smoke - I jumped for joy when I found out he was in and I'll be learning every in and out of his playstyle that I possibly can.
Sorcerer: Kenshi - Some of the levitation-heavy combos I pulled off with this guy litterally made my friends' jaws drop (on occasion, the timing of the post-uppercut tele-slam was brutal). Definitely a piece you want to able to protect against absolutely anything.
Champion: Ashrah - Since it's still the "queen" piece, I feel obligated to get good at playing one female character. She has a great look and nice moves, so I won't mind learning her combos.
Leader: Sub Zero - I almost never played with him against my friends since I essentially never lost (unless I was trying to get better at his shotokan style) by linking insane combos to each and every freeze. He'll be even better with ice clone and he's definitely going to be my King piece.

I'm pretty excited about versus mode at this point. Hopefully it will have thorough stat keeping and not be ruined by cheaters.