My husband says I am the last refuge of the geriatric equine, so I'm biased. But no, 14 is not generally old by horse standards. But as PP have noted, a lot depends on the individual's conformation and the way he's been used in the past. The guy I train with has a lovely horse on loan from a friend for students like me to ride. Horse is about 16, and had a long, successful career as an advanced-level eventer, and still fox hunts on a regular basis. It is incredibly well-trained and has a generous temperament. He has some arthritis type issues emerging, and I'm sure his X-rays would be, um, interesting. But for a horse that has gone that hard, he's astonishingly injury free. The trainer attributes it in part to a certain economy of movement the horse possesses. Says it probably has protected him in the long run.
Don't buy a horse with just a few weeks of lessons under your belt. Bad idea. Dishonest sellers will smell you from a mile away. Lease a nice horse at your lesson varnish for awhile and enjoy the positive aspects of horse ownership without having to deal with mind-boggling expenses and 3 hours of chores a day