B.W.
Look for a 'beginners' DSLR. Now days you can find a great DSLR for a reasonable price. ANd you are good to want one, the delay is almost nonexistent on them, so you never miss a moment.
I shoot Nikon (I'm a photographer) and have owned everything from the very old film SLR's (that you had to wind the film yourself!) to a D300. I use the D300 now. A great entry level DSLR for a Nikon is a D40x, or a D80. You can find a used D50 or D70 for $300 or around there. Both are excellent camera's that will suit you well.
If you prefer Canon, you can find an XT or Xsi. Again these would suit you well with the camera and kit lens for snapshots.
Find a camera store in your area, they likely have used camera's that have been factory serviced and are in pristine condition, and you can get them for a very reasonable price compared to new, and its just as good. I've purchased 3 used DSLR's and have never had a problem with them.
Purchase a camera with the kit lens. ITs a basic zoom lens that will suit snapshots well. If you want to learn more about shooting an SLR camera, picku p the book 'Understanding Exposure' by Bryan Peterson. It will teach you the basics on using your camera outside of program/auto mode, and how to shoot creatively.
Good luck!