As mentioned, search out lesson barns, therapy barns (Volunteer work looks great on college applications btw.) and once you have some more experience see about maybe farm sitting for money.
I'd also recommend doing a lease of some kind first, before you buy. This gives you a great idea of how you would have to rearrange things in your life to be able to care for the horse. You may find that waking up at 4 AM to feed the horse and muck out isn't really your thing, or maybe it is, you never know until you try. But I'd get some lessons under my belt before doing a lease, as it will be someone else's horse you'd be caring for.
If you don't already work, look into a part-time job and/ or a summer job. This way you can put away money far ahead of time.
I know some high schools offer credits for students who work, so this could help you financially and school wise.
I've mentioned it on this forum before, but one of my favorite ways to help people out and make a little extra cash for lessons is to donate plasma, it takes about 2-4 hours per week and you can earn $200-$300 per month doing it 'full time' (2 x per week every week, as you'll only get about $25 per visit on a type of debit card.) But to get the money you must donate the plasma, blood only gets you a cookie, and of course the happy knowledge that you've helped someone in need.
Good luck with everything.