I will try and answer your questions:

You should most definitely pick up at least one extra controller. The Wii only comes with a single controller, and while some of the games on Wii sports will still allow multiplayer by simply handing the single controller to the next person, it is best to have two.

As for memory cards. The Wii includes 512mb of flash ram space to store stuff. What that means is that the Wii basically has several thousand blocks of memory built into it to save games and store any downloaded content. I did pick up an extra 2gb SD card for my Wii. But thus far it is basically useless. The Wii games do not yet have the ability to access the SD card slot for saving games so it is really only used more for backing up anything you downloaded to the Wii.

Far as I know the Wii is 100% compatible with all Cube games. So you shouldn't have any trouble at all in that regard. The Wii includes 4 cube controller ports for Cube gaming and also two Cube memory ports to use Cube memory cards in as well. I only have and use Nintendo 1st party memory cards in my Wii and haven't had any issues. But I've heard reports of people with 3rd party memory cards from Madcatz..etc having problems using them in the Wii. Also you can use Nintendos Wavebird controller just fine in the Wii.

DVD functionality? Here you are out of luck. The Wii doesn't have the ability as yet to play DVDs. Not sure if it will ever be added. There was talk not long after the Wii was released last November of Nintendo planning a 2nd revision of the Wii that would include DVD playback. But this was only to be released in Japan and there wasn't any talk about a US release of this version of the Wii. However, most seem to agree that since the Wii is using a DVD-rom drive the physical aspects needed to play DVDs is there. The Wii just needs software added to be able to access and play them. So perhaps a future download might be possible for this for a fee from Nintendo.

As for some games to pickup? That depends on what games you really intend to play. The Wii doesn't really have any hardcore gaming type games for it yet except Zelda. But if you have the Cube version then there isn't much point in getting it again for the Wii honestly.

But the games I would recommend are the following:

Zelda = Excellent adventuring to be had here.
Elebits = Lots of fun, unique game and really shows off the Wii-remote abilities.
Trauma Center: SO = Basically a redone version of the DS game with a few more missions as it were. But great use of the remote once again!
Sonic: Secret Rings = Probably the Best 3D Sonic yet gameplay wise. Good graphics for a Wii game thus far.
Super Paper Mario = This is an excellent game as well that is easy to play.

Honorable mentions would be Harry Potter:OOTP for Wii as I really enjoyed playing that one and thought it was pretty impressive graphically. Also, I would recommend Super Swing Golf. It doesn't play too much like traditional golf but I think it controls better than the Golf in Wii Sports, and really enjoy the ease of play and variety of courses it has to offer.

Hope this helps?