The main difference in digital cameras these days is the weight! Get one that's light enough not to weigh you down. You can get a decent smallish one that's perfect for on-screen viewing for about $100.
The other thing is to get one that's suited to your needs. Some have too many high-end-like features that can just be very confusing... it makes a huge difference if this is a replacement for a life-time of "real" camera useage." If you already know what aperture priority, etc, is... then go ahead and make sure you have all those features.
If you are going to make large prints from your shots, then you'll want to have at least a 5 Mega-pixel version. These will cost between $600-1,000. (They're making 10-12 mega-pixel versions now!)
If you're only ever going to show pictures on a lap-top or to your TV set then you don't really need all those extra expensive Mega-pixels. More Mega-pixels means the photo can be printed larger without losing the crispness and focus of a clear image. (that means higher "resolution" - see the article above!)
I don't really have a favorite brand. I've seen some FUJI models demonstrated that are very good, easy to use and good price-ranges, and some cameras come with all sorts of computer add-ons you might or might not need/use. I have a NIKON that I really like, but Canon gets high ratings too.
If you're interested in seeing the options out there, and you're not intimidated by a salesperson trying to sell you something, I'd recommend walking into your local Camera shop, and asking them to show you the various levels of digital cameras. They're usually very knowledgable and friendly. I didn't buy mine there, but they were very helpful in showing me the various options, styles, and you can feel how heavy it's going to be!
When you're ready to BUY, take note of the exact model name and number and shop for the best price online at sites like :
Make sure you get an extra memory card at the highest quantity you can. It's worth it to have a 1GB card in the camera to swap for the dinky little 32MB one that might ship with the camera. Also an extra battery is a good idea, when you're on a trip and the battery goes, you don't want to wait several hours for it to recharge.