Start saving to buy a horse now. By the time you can comfortably afford it you will have much more experience under your belt and should be able to purchase a pretty nice horse!
I know how desperately you want a horse, I went through it, too. But you have to realize it's not meant to be just yet (:
Also, the cheapest part of a horse is buying it! You will be shocked at how much a horse needs!
My mare needs to be shod every 7 weeks, have her teeth floated once a year, get dewormed twice a year (maybe more), goes through flymasks and fly spray like crazy, has the chiropractor out every 6 months, and has an annual vet check. That doesn't include the two saddles, two girths, two pairs of leathers, irons, bridle, two bits, bling browband, four saddle pads, bathing supplies, two whips, lunge whip, four lunge lines, overflowing bag of brushes and hoof picks, and my own riding clothes!
You'll get your own horse someday, but for now enjoy leasing and learn as much as you can!