I've decided to get a Wii. This will be my first console ... ever.
I'm fairly clueless though seeing as how I haven't paid any kind of attention to the console market ... ever.
So I need some tips about what to get with it. I figure I'm going to need an extra nunchuk for playing with friends, a classic controller for downloadable NES and SNES titles, and probably some more accessories I haven't even heard of.
In addition I'd like to get some tips as to which games to pick up. Okay, Super Mario Galaxy and Legend of Zelda are pretty much mandatory extras. But what other games are worth getting on the Wii? I'm stuck with the impression that there are very few quality titles on the system so far.

Red Steel is a great buy. And of course, since it's your first console ever, pick up a Rock Band game so you can embarass yourself among friends.
Oh, and, uh, um, Punch Out.

What genres do you like?
Edit: This list can be a good start

Dude, recommendations from /v/? Are you insane?
Get the Telltale games from the WiiWare thingy. They're really good on the PC, and it can only be as good on the Wii.

As a long-time lurker of /v/, yes.

As a long time lurker of /ck/, you burn in hell.
Actually, I haven't been on 4chan in ages. Ages usually means three hours ago.

While my first advice is to not buy the Wii at all and buy a PS3, I will give you some sort of idea of what games are good. I used to have one (before I sold for PS3 money).
The Conduit, while overhyped by fans, is still the best shooter on the Wii to date.
Super Smash Bro's Brawl
Super Mario Galaxy
Legend of Zelda: Twilight Princess
In my humble opinion, the controls on Red Steel makes it a deal breaker for me.

I'm not getting the PS3, at least not now.
Wii's main selling points are simple. Mario and Zelda. That alone dwarfs the competition. PS3 has superior everything but I can play killer games on my PC instead.
The Wii I'm getting to play fun, relaxing, and/or social games right in my living room.

Please... Do yourself a favor and don't get Red Steel...
As for other games you should get:
Bully: Scholarship Edition is great on the Wii. Controls are responsive and all the motion controls make the game more engaging.
Super Smash Bro's Brawl for sure.
And games from the Virtual Console and WiiWare as there are many, many old gems in there that would be worth buying.

No More Heroes?

Well, I would say to get a Gamecube controller, since I don't like the Classic one that much. Plus, I don't think you can play gamecube games with the classic controller.
As for the games, you should get:
Metroid Prime Trilogy
Super Smash Bros Brawl
Super Mario Galaxy
The Legend of Zelda: Twilight Princess
And there's still more, of course. But then it's a matter of taste. Like Wii Music, Mario Kart Wii, Animal Crossing City Folks, etc. Some people love those (like I do), but then some people don't.

If you like Zelda then I'd also recommend Okami.

Red Steel? Are you insane? That is a horrible game. Terrible AI, controls, story, acting... it's a pile of junk.
Punch Out's awesome, though. Get that. Also, Super Mario Galaxy is amazing. One of the best platformer's I've played in a while. Get Zack and Wiki if you're a fan of adventure games. WiiSports Resort has a small set of minigames that are a blast to play, and hold well for endless playthroughs. If you like lightgun games, The House of the Dead: Overkill, Resident Evil: The Umbrella Chronicles, House of the Dead 2 & 3 Return, and Ghost Squad are very fun. If you like FPS games, get Metroid Prime Trilogy, because all three games with Wii controls for a $50 price tag on one disc is amazing. If you enjoy racing games, I wouldn't know much because all my racing games are on PC, 360 or PS3, but I've heard good things about Mario Kart Wii.
The nice thing is if you decide to subscribe to GameFly, most of their Wii games aren't heavily rented, and you can buy their copies from them once you have it in your house and know it works well, if you really like the game. It also lets you play games that you probably would never want to buy, so you have money for the games that you feel are worth buying new.
EDIT: Ah, but you're in Norway, so disregard the last paragraph. Whoops!

As I said in the original post I will of course get Super Mario Galaxy and Zelda.
I'm looking for other games. Metroid Prime Trilogy I will also get though.
Anybody tried Dead Space on the Wii? It's pretty new.
And are there any other accessories I'm likely to need? I don't live near a store that sells Wii so I'd like to stock up on stuff in advance.

http://www.metacritic.com/games/wii/scores/
WiiWare might have a larger library of quality games than retail. :P
LostWinds seems great...