Bonnie,
I am not the most knowledgable person about cameras but I work in a store that sells them so I know a few things. A 10 megapixel camera will give you lots of flexiblilty for enlargements and photo editing. For instance, you'll be able to crop out a portion of a picture and enlarge it and still have really good picture quality. Make sure the zoom is "optical" zoom and not "digital" zoom, most cameras now will be. Optical zoom gives you the best picture quality. I like cameras that have a viewfinder. If you do not have a viewfinder and have to depend on the screen only you may find you have glare issues outdoors and it may be hard to see the image you are actually capturing.
Consider what kind of batteries it uses. You will find a lot of differences. If it is rechargable, check how it charges. I bought one for my daughter thinking the box included an AC charger and found out it charged through the computer with a USB cable. I ended up buying the AC charger separately. I use a camera that takes AA batteries and that is what I personally prefer.
Make sure you get a memory card. The one that comes with the camera will only hold a few pictures. The good news is that most types of memory cards have come way down in price. This is a great time to shop for cameras because most places have them on sale now.
I hesitate to recommend a particular brand, I'll leave that to someone else but I checked out one of the new Nikons the other day and was really impressed with the screen clarity. Mine is a Canon Powershot and I really like it, very user friendly. Hope this has helped a little.
Mechele