[elgyqc]

Be clear on what you are getting into if you buy a 986 Boxster (this applies to everyone, not just you). You will be getting a car that is 18 to 25 years old that will need to be maintained. Even the best example with maintenance up to date and no current problems will need work as old parts wear out, rubber hardens and things break.
You can pay someone to work on the car or you can do it yourself with the help of friends and family. If someone else works on the car it will be expensive and you will need income to pay the bills. If you do it yourself you will need a place to work, tools, time and mechanical inclination as well as money for parts. You should factor in the possibility of a major failure like a blown engine which can transform a $12,000 car into a $5,000 boat anchor. If you can find and install a used engine you could get it moving again for a minimum of, say, $4,000. If you pay someone to do it you can double the price.

At your age I dreamed of owning motorised vehicles... started with motorcycles and had to change the engine in my first car, a Triumph TR3. I grew up on a farm with space to work on my vehicles, some tools and a fascination with all things mechanical.
Not everyone wants to, can or should go to college. Some young people get actual jobs that pay well and where they take part in producing useful things for society, only you know what your situation is, but think about that.
You didn't mention where you live, where I am my Porsches or stored from December to mid March at best and from November to April if the winter is drawn out. Being without a car for up to five months of the year is a drag... but it is a good time to catch up on repairs.
If you can keep enough of your original budget to pay for parts for the years before you have a regular income and you have the necessary things mentioned above to do your own work with help from those around you than it could be a fun, learning experience. Fifteen year old me would be very jealous if you can pull it off.
Otherwise I would suggest something more mundane. Toyotas are in general bullet-proof and cost less to maintain... and there is room for friends. If you only have one friend a Miata is like having an underpowered Boxster that is a lot less trouble.