I actually own all of the games you said :P
First, let me say that the 2 screens don't hinder anything for any notable game.

Tetris DS is a budget title. And it's Tetris. And you can play with 9 other people from around the world AT THE SAME TIME. You can also play with 9 other friends in the same room using just one DS cart. The extra modes are interesting, but you can totally ignore them and enjoy the game. Get it.

Bleach DS is a Smash Brothers style anime fighter (I think it's made by Treasure) that's pretty enjoyable if you're a fan of the show. It's completely in Japanese, and the WiFi is passable. The one time I played it WiFi it was laggy as hell, but then again everyone who has this game is in JAPAN and I was probably downloading an episode of Bleach at the same time :P I don't know if you'll find anyone playing Bleach on WiFi much, as the game has been out for a while and it doesn't exactly have the same longevity as Mario Kart or Tetris.

Kirby is the first 'real' game for the DS, and it was bloody awesome when it came out. It's still really good now, and the touch screen doesn't hurt the game at all (only if you suck at drawing lines). It has some pretty nifty unlockables (songs, characters, different colored lines) and a good bit of challenge. I've had the game since it was released, and I still put it in from time to time.

Sonic: I haven't really played it much. It's pretty cool, but I got it around the same time I got Jump! Superstars so it was kind of pushed out of mind :P

Big Brain Academy is a very fun multiplayer game that anyone can play. I can see how it can be addictive, but I've tended to avoid those behaviours since I went cold turkey from Oblivion a few months ago.

Mario & Luigi is enjoyable and pretty funny at times. I haven't finished it yet so I can't speak on its length, but I think I'm about 13 hours in. It doesn't use the touch screen *at all*, which confused me at first. It's not outstanding really, but recomendable. If you played the previous game then it should be an automatic buy.

Advance Wars is a 'get', for sure. I actually have it in my DS now, I've been playing it again for the last week or so. If only it were online....!

Ok, so I'll rank these in the order of getting (if you're gonna get 'em all anyway)

1: Tetris and Advance Wars (yes, together)
2: Big Brain Academy
3: Kirby
4: Mario & Luigi
5: Sonic or Bleach (don't know Sonic well enough, and Bleach is purely optional)

If you play multiplayer a lot (not just WiFi), Bomberman is another game to get as well. Mario Kart, Big Brain Academy, Tetris and Bomberman are some of the best multiplayer games for the DS.
If you can get a few people to pick up 'Jump! Superstars', that could be pretty awesome as well. It's like a fully customized Smash Brothers using the characters from the Shonen Jump manga (Dragon Ball, Bleach, Naruto, Kenshin, etc). In order to get the most out of the game (if you don't read Japanese) you'll need to consult some FAQs to match the pieces to unlock stuff. It's a cool game on its own, and once you do beat/unlock everything it's like playing through Smash Brothers' mission mode over and over.

Hope that helps.