I'd also like to suggest getting your own horse if at all possible. School horses are great to learn basics and small jumps on, but once you start getting to the bigger jumps, most trainers won't want you to jump over 2 ft on their horses because they are usually older horses and they don't want you riding them to the ground.
There’s no specific amount of time it takes to begin show jumping. It simply depends how much work and time you put into it. Before you begin jumping, I’d suggest having gotten the walk, trot, and canter transitions down and comfortably be able to both sit and half seat all three gaits. Show jumping takes time to learn, however, the amount of time it takes all depends on the rider’s will and determination. I hope this helps.