Good questions! Well I would be buying an older horse and the uni I want to go to has stables on campus but if I change my mind by then, I will probably lease my horse or keep him/her as livery at the riding school I am currently at. There is a horse vet near me and a farrier too. My parents are willing to pay for a horse when the time is right. I also do have the time to see my horse after school for a few hours and I know that they need to be checked on 2-3 times per day so I will do what a lot of other girls at my riding stables do. That is basically being a full livery. So they feed, groom and water your horse as well as turning them out and you pay for a normal livery price where you buy your own stuff. In return for the deal, your horse is used a riding school horse for others to ride for lessons.
This is what my family did when we bought our first, and second, horses. Our horses were "boarded" and in exchange for letting them be used in lessons, we got a slightly reduced fee.
But, also in order to save costs, we cleaned our own stalls (it was an extra $20/week to have them cleaned for us). That meant that we were at the barn at least 4 times every week to clean two stalls. Horses are wonderful
but they are a full time commitment... all my teen years, I spent most nights at the barn until 10 or later, doing homework on the bus and in the car so I wouldn't have to stay up. Most weekends were at the barn, or at a horse show during the summer. 
What I would suggest, assuming your parents are also considering a horse for you, is to first do a "lease." That is when there is a horse that somebody else owns, but you are paying the expenses for... and in exchange, you get to ride the horse and get full access to it like it's your own. There's also "split lease" where maybe you pay part of the board and get to "have" the horse a few days a week. It's a great way for people to test out horse ownership
We did this with both of our horses at different times - for example, a family with 2 little girls paid half the board for Emmy and got to "have" her 3 days a week, plus took her to shows.
Definitely, if you're looking into getting a horse, talk to your parents and talk to your trainer. Maybe your trainer knows of a horse already in the barn that you could lease
One last note.... when your family starts looking to buy, best make sure there is a stall available first! 