It sounds like your parents not only have the resources to fund your new interest, but also the willingness. Therefore you are in a very envious position for many people. Take advantage of it, responsibly. Sign up for lessons at the centre near you and see how much you enjoy the sport. You have to enjoy the good days enough to make up for the bad days, because there will be bad days and there will be bad horses, bad trainers, bad falls, bad weather... Well, some people are lucky and don't see so much of the bad, but you have to be prepared for it, JIC.
Sign up, read, listen, ask questions and gain experience. When/if you are ready to lease or buy your own horse, you will be happier for it.
Good luck and welcome to the forum!