For your first horse, you want the most dead broke horse you can find, and make sure he/she has good ground manners. Quarter Horses and Paints are usually pretty easy going, but all horses are individuals and might not conform to breed standards. Individual temperament is more important than the breed. Age is important, too. I wouldn't get anything younger than about 8. You want a reliable horse that's been there and done that. I learned that the hard way, and I was your age when I got my first horse.
Trying one out for a few weeks is highly recommended. That way you get to see how he'll react in the new environment and you'll really get the feel of what you're potentially buying. It also eliminates the worry of a horse being sedated when you go to look at him.
If you don't plan on showing, the horse doesn't have to be an over-the-top stunner, although looks are always a bonus. I'd also recommend having an experienced horse person go with you when you look at horses. And LISTEN to them when they tell you "yea" or "nay". They tend to know what they're talking about. ;D
I would definitely steer away from Thoroughbreds and Arabians, though. They're hot-blooded and energetic, and just too much horse for a beginner. A lot of them are flighty and unreliable, as well. Not all of them are like that, but it's pretty iffy. It's safest just to stay away from them until you know what you're doing. Fjords, Haflingers, and Welshies make great first horses, in general.
There are some nice grade horses out there, too.