I received a pre-Christmas note from a friend on which camera to buy and I thought about it and wrote back. FWIW, I'm sharing my thoughts ...
On cameras, the brand I've worked with is Canon. It's been good. I went there because I thought the digital color was strong and pro usage is pretty extensive ... though of course there are flame wars between Nikon and Canon. Both brands offer exceptional options. Here's what I've looked at and work with --
Point and Shoot -- the top rated two options are the Canon G10 (now the G11) or the Leica D-Lux 4. I bought the Canon G10 for about $500 and subsequently lusted after the Leica for about $700. (The Leica has some awesome image quality for a small camera and a certain elite appeal.) However, as I got used to the Canon, my lust faded. Leica, while nice, is too "precious" ... not as sturdy as the Canon, no auto lens cover, a little harder to set. The Canon G10 or G11 gives you a lot: Great image quality, the ability to shoot in RAW format (and, subsequently, edit/post-process native image files without loss of quality ... this is really important to me). Plus it has a pretty bomb-proof metal case and feels okay in the hands.
On the digital SLR, there are a lot of options. I started with Canon's Rebel for about $500, and moved up to the 5D (which cost new about $3,000). But, really, many Canon SLR bodies will be just fine, particularly as you get started. The key thing that makes the difference is the quality of the lens. The kit lens I got with the Rebel was pretty weak, about a $100 thing ... the images were never very sharp. My first higher end lens was the Canon 70-200 F4L, about a $600 deal (non-I/S). The damn thing delivers great results, all my shots at bike races (including candids) are from that lens, both on the Rebel and the 5D. Subsequently, I added the 24-70 F2.8L (the wedding "brick") and I'm probably going to get the 135 F2L before my next overseas trip. So, I'd recommend a reasonably inexpensive digital SLR like the Rebel or a used 20D or 30D, and spend more money on good glass -- which you'll keep using if you move the camera body up the food chain.
One advantage of the point and shoot is that it is portable and mostly self-contained -- e.g., it has its own flash, no need (or ability) to change the lens. The SLR is more complicated (and more capable, as you grow ... some pros, though, like Chase Jarvis think the iPhone is the best thing since sliced bread (mostly because it's easily ubiquitous ... if there's good light).)
There are lots of review sites out there. I think Fred Miranda is among the best -- http://www.fredmiranda.com.
So, these are my starting thoughts. Get something you like, that feels right, and shoot a lot. Henri Cartier-Bresson, my favorite photographer, said something like "Your first 50,000 shots will be bad, so get them over with." It's a great art form, and way to remember things you like, your family, the mountains.
The other piece of the equation is what you do after you take the pictures. I discussed this here.
Anyway ... I hope you have a great holiday and that photography brings you as much satisfaction as it does me.