No one has suggested Mario Galaxy. This was an amazing game, one of the few over the years I couldn't put down.
Yes, definitely invest in the rechargeable battery packs so you don't have to constantly be buying AA batteries.
The Wii Sports package it comes with is a great start and will keep you entertained for a long while even if you don't buy other games.
I've also enjoyed playing (in no particular order):
Wii Fit
Paper Mario
Raving Rabbids (I and II) but the first one more
Tiger Woods Golf
Super Smash Brothers (with a lot of people)
I didn't enjoy playing Resident Evil, I just couldn't adapt to the controller setup, but then again, I somehow missed the tutorial in the beginning and had to "figure it out".
Also, Wii Play, that comes with the controller is rather boring. Yeah its only $10 more than the controller pack itself, but IMO not really worth the $10.
Based on what others are saying, I think I'm going to get the Lego Star Wars game soon. Sounds like fun.
One of my favorite parts of the Wii is the Internet connectivity to your friends. You begin by designing your Mii's on the Mii Channel and set them to "Mingle".
Then, (set up your internet connection) go to your message board and go to your address book. It will show your your Wii Number, call up your friend with a Wii and ask them for their number (or send a note to email over the Wii) Once you exchange Wii numbers go to the Mii Channel.
There is something called the Mii Parade. It doesn't happen instantly, but eventually the Mii characters your friends created will "show up" in your parade. You can then choose people you want and "drop" them into your Mii Plaza.
The Miis will now show up as your competitors in games you play, or spectators when you play tennis, as statues in Mario Kart, etc. Its pretty fun.
Well that's all I have on the subject, back to "work"