There are a number of things you should look at when looking for a digital camera.
1) Shutter speed is definitely one of them, BUT that is solely used if you want (and are going to utilize) action shots.
2) Another item is the number of megapixels. 3 megapixels on up is good for pics on the web, and regular prints. 5 megapixels on up for printing on 8x10s. Anything over that,...and you're talking small to large sized posters. The thing is though...you can ALWAYS go down on resolution, but you can't go back up.
3) Also, look at the batteries. The use of a flash consumes a lot of battery power. Also, determine whether you want batteries provided by the manufacturer OR whether you want to use a camera that utilizes a standard AA battery. Personally, I would go for a camera that uses it's own battery. They last longer. You also may want to consider purchasing more than one extra battery. (I literally have 4 extra batteries for my camera, because I used to frequently attend automotive events and take TONS of pictures).
4) The use of extra lenses. Check to see if you can use other lenses w/ your camera. Small, more "personal" and recreational use cameras usually do not come w/ this feature. Larger, more serious type cameras come w/ a variety of lenses to choose from.
There is tons of info to know.
Definitely go to a reputable camera store and ask for more information. Don't be afraid to ask questions.
Since you live in SoCal, here are some great photo shops that I know of:
Paul's Photos (
www.paulsphoto.com)
Silvios (
www.silvios.com)
These two shops are great and a favorite among the professional photographers in the South Bay area.
Here is a great site for reviews on cameras:
http://www.dpreview.com/ http://www.bhphotovideo.com/ (great prices)
Also, consider going to say Borders bookstores and flipping through the various photography magazines.
My personal recommended brands are either Nikon or Canon. But the Sony cameras are great for the money.