How long should I take lessons before getting a horse?

As a teen I rode horses of every description from a 13 hh stocky part Welsh to a huge Belgian. They ran the full gamit of dispositions. Mostly I rode OTTBs since there was a big racetrack nearby. By the time I was 18 I could handle anything a horse could dish out. I desperately wanted my own horse but had I gotten one, in hindsight, I learned far more than I would have if restricted to one horse. Horses are retrainiable and when you become a skillful rider you will be less concerned about a prospective horse's training and can focus on his conformation and health.

thats why so many 17 hand horses do barrel racing and reining events ? Sorry but you know not of what you speak.

^^^ They don't do well in barrel or reining because the longer legs make it harder to do those sharp turns. Horses lower to the ground will naturally be able to make tighter turns and spins quicker because of their lower center of gravity. It's like asking why you don't drive a lifted jeep in NASCAR. Apples and Oranges.

That being said... To OP, I'm a tall horse girl myself. I like them 16hh or bigger. My gelding is 16.2 and I love him. He is very easy for me to ride. A little hard to get up on but I just have to keep in shape so I am able to mount up as easily as possible. Good motivation to stay fit.

I didn't have a single lesson before I got my first horse. Mine was an OTTB that was given to me by my grandfather. However, my father-in-law, has ridden his whole life and was there to give him a test ride in the round pen before I took off on him. I've learned as I've gone along. Comic has learned right along with me. "A lot of wet saddle blankets" is what my FIL told me. We took a few lessons about a year after I got him but other than that it's just been trial and error and listening to advice from others.

Be patient as you try to find the right horse. I think you could start looking now if you wanted. Ask your trainer to help you look at horses. I think it's good for a person to learn with the horse they own. Nothing wrong with lesson horses it's just a different kind of bond with your own. But take your time and look at lots of options. When you find the "right" horse, that you and your trainer agree is the one, buy it. Doesn't matter if you are 2 weeks or 2 years into lessons IMO.

Perhaps you might want to evaluate that statement for how it might apply to yourself?
The height issue in relation to participation in those events has nothing to do with how easy they are to handle or ride and everything to do with the fact that their lower center of gravity and heightened ability for tight maneuverability making them more suitable for those activities.