see if there is anyone at your barn open to a half or full lease! if you are fully committed for a year after having your own horse to take care of, ask to buy
You can try raising money by yourself. Maybe if they see your dedication they will help you financially
Try leasing first and if that goes well then buy one. There are horses you came lease from another farm so the it is kind of like owning one and the lease is usually a long time.
Starting out with a lease is a great idea! I started leasing my horse last June and ended up buying her in January. Just make sure it's a long term lease and it's best if it's not on a lesson horse/pony, try finding one to lease that not many people ride so that eventually you may be able to convince the owner and your parents to buy!
Maybe try to persuade them to let u lease first! That's what I did then once my parents saw how much attention I was giving my lease horse called fritz they got me my own horse called molly which is the horse I have today