If you have no desire to train a horse or have a green horse (young inexperienced horse), then you ought to look at buying a horse that is around 5 years and older. That way the horse has had a number of years where he has been ridden and taught. If you are looking to learn a particular sport and compete, then it could be to your advantage to buy a school master.
This is an older horse that has successfully learned and usually competed in a sport and is looking for a little less action. The owner may not think the horse is ready for retirement and would be an excellent teacher for a beginner rider starting out. Depending on the age and health of the horse, you could learn and begin to compete on the same horse. Or you could learn on the older horse and buy a younger horse once you start competing. Of course that leaves you with another question of what to do with the older horse?
How much can you afford to spend on the horse? This question helps you decide whether you buy a young horse, an older horse, or even a foal. If you are seriously looking to compete you may be more concerned about bloodlines. Bloodlines relate to a horse