Low budget:
1. Modify the airbox to take more cold air. Instructions are on the forum someplace.
2. Get a muffler shop to put a magnaflow muffler and new tip on. Mine cost me about $175. Sounds great and should free up some flow over the old exhaust (making an assumption here). BMW cats usually flow pretty good, unless yours is bad I'm not sure there is going to be a big gain there. If somebody has tested this and found otherwise - chime in.
3. Mark D chip.
4. Remove weight. Cheapest HP you can get, because it doesn't cost much or anything. Pull out crap in the car you don't need. For me that includes the spare. If you buy wheels and tires don't get cheap heavy ones. Pay close attention to what they weigh. Rotating mass robs more power than you can gain on all these other tricks combined.
5. Tune up. New plugs, wires or COP, airfilter, etc will regain a lot of lost power. Buy a good quality air filter like Mahle. They seem to flow as well as expensive oiled cotton ones. At least according to some testing also posted on this site.
6. Junk yard upgrades. Swap the diff out to get LSD or more acceleration. Single mass flywheel upgrade. M50 coils. Mustang injectors. Search the forum for instructions and advantage/disadvantages of each.
All of these should be doable on a teenagers budget. The most expensive item is the Mark D chip (unless you go looking for new wheels and tires.)
Good luck and enjoy the BMW.