Hi Moose.
At the risk of sounding facetious, I would honestly say "get both"

, but if you're going for strictly one or t'other, I would go for......
Wii = great family games. No need to huddle in a bunch to see the screen. Unlikely to get damaged/dropped by the littlun.
DS = great family games. Portable, so can even play it in the garden. Very cheap at only ~£100. Cheaper games too.
On balance, I'd go for the Wii first. Even if you just stick with the bundled Wii Sports, it's packed with 5 great mini games and, despite the "proper" titles being released throughout 2007, Wii Sports was still my most played game of the year.
After using it during 2008, later on I would then consider a DS (e.g. next Xmas) as an "extra" handheld to have around.....but I think the Wii will do fine on it's own initially

.
Starter games for the Wii that everyone will love would be:
Wii Sports (included)
Mario & Sonic at the Olympics (lots of family orientated mini games)
Mario Party 8 (another family orientated bunch of mini-games)
WarioWare Smooth Moves (I hated this but MANY people absolutely love it - dozens if ultra-mini games here)
worth a cheap 2nd hand punt (£10-£15) = Super Monkey Ball Banana Blitz (not as good as the above, but worth it all the same especially at the 2nd hand (and even "on sale") prices I've seen it at recently - the game is over 1 year old).