Great question! I suggest going to the nearest best buy and "play before you pay." You definitely get what you pay for.
Do research before you purchase your first "baby."
Looking for something small and pocket worthy? I suggest the digital cam, "Cyber Shot." (and get the highest mega pixels possible-highest mp creates the most clear results!)
My first camera was a Cannon, and I never looked back.
I reccomend Cannon, because the set up is beautiful, it's really simple to use and the instructions are step-by-step and easy to follow. (Again, go for the highest MP possible, of course, the higher the MP, the more the camera is apt to cost too.)
It's all about experimenting, and getting comfortable with your equipment, from there, it's about a relationship. You be nice to your camera, and it returns the favor of awesome quality snapshots.