I'm fairly new to digital photography myself but here's some advice you might want to consider.
My first recommendation is to look for something with 3.2Meg resolution (price range should be around $300 - $400). This should give you enough detail for most of your needs--prices jump up quite a bit if you move to the next level of cameras at 4Megs (not bad at all if price is not a consideration and you know that you will be doing lots of 8x10 plus enlargements).
Next, buy the smallest camera that you can comfortably operate. If it's convenient to carry, you will use it more often.
Also, don't fall into "the-more-bells-and-whistles-the-better" trap. Just look for basic features that are intuitive and easy to operate without constantly referring to a manual. It should go without saying but I'll do so anyway: a 2 - 3x optical zoom lens is a must (fortunately this should be standard on most cameras with 3.2M).
Look at the type of storage media (card) the camera uses, then look at your computer (if you'll be using one to process pictures) and/or your current printer (or future photo printer) so you can match up the compatability of the cards and slots. You might also want to look at the maximum storage capacity the type of card can hold and its cost relative to competing card types. Don't underestimate the importance of this exercise.
Consider the type (or types) of batteries that the camera will be using. Rechargeable nickel metal hydride batteries interchangeable with lithium batteries are ideal. I don't care for proprietary batteries that is only made by the camera manufacturer because they're usually more expensive and may be hard to replace when you're on a trip.
Finally, I used to be a loyal Nikon fan with film photography but with digital photography my preferences are Canon, Sony/Olympus (tie), and then Nikon (in that order). Digital Elphs, A70, and S45 (all Canons) are cameras you might want to check out.
My recent (and first) digital camera purchase: Olympus C-750 Ultra Zoom. Do as I say--not as I do!
I hope this helps you.