There are so many variables in my mind, that asking what camera would be good is like asking what shirt is comfortable.
Are you looking for a small camera to tuck in your pocket? Are you looking for a lot of features so you can grow with the camera once you learn the basics? Do need a camera that comes with image stabilization? Do you want one with a movie mode? How will you be using your pictures? Will you only be sending them by email and printing 4 x 6 or will you be needing larger sized prints?
The first thing I would do, is check out some review sites. Here are two to get you started:
CNET Reviews - Here you can sort by price, manufacturer, resolution etc.http://reviews.cnet.com/digital-camera-reviews/?tag=bc
Pick 2 or 3 cameras that you like and then take a trip to your local camera store. Make sure you actually pick up the camera and take some shots. Some cameras sound great, but are too small or too big and the buttons/controls are hard to handle. You have to feel comfortable in handling the camera. Ask one of the staff there what they recommend.
I'm a Canon/Nikon fan, but there are many great valued cameras out there. It all depends on your own needs and what options you want your camera to include.
Also, when you buy a camera, remember that you will probably be upgrading the memory card, buying an extra battery/charger and you usually want to buy a case for it as well. These all are extra, so make sure to factor that cost into the price as well.