The advice I will give you is to be certain you can afford a horse. They can be expensive when you factor in feed, vet bills (and there will be vet bills), boarding and tack. Then you need to be sure that you know what you want to do with the horse. As others mentioned the quarter horse is a fine choice but know that whatever horse you get you are not a passenger. Riding requires constant communication between rider and horse to be done properly. Above all before you lay money down for a horse put out about $1500 to have the horse thoroughly vetted. Try the horse on a trial basis. Many will medicate a horse to make it seem calm and then, depending on the medication, a day to two weeks later you have a very spooky horse on your hands. Having a horse is a huge responsibility. Do your research.
If you are a new rider, I would advise you to buy the American Quarter Horse. This horse is very adaptable, well-liked equine breed and it is good for new rider. Their breeding ability has made few stud ranch owners both well-known and rich. To learn more about horses visit http://www.horses-and-horse-information.com/horsebreeds.shtml.