your two best options are a miata or an e30. both are very reliable and pretty fucking quick on the track for their price.
e30's are a little quicker stock. a 325is with HR race springs, new shocks, and a good set of track tires will be awesome and cost you well under 7 grand. leaving you money to spend when shit goes wrong.
to be honest though, a miata is your best bet. you can find them in awesome shape for like 3 grand, there is a huge and CHEAP aftermarket parts supply for them, not to mention spec miata is probably THE most popular class in the US, and the miata is by far the most common and used track car, for good reason. you can find a butt load of knowledge and parts that apply to tracking your miata also. get a set of the spec miata coilovers which are pretty cheap. a roll bar, racing seats, exhaust, intake, some legit track tires and wheels, and you have one of the best possible track cars for under 20,000, but you spent 5. i tracked my friends miata with coilovers, r comp tires, some bracing and a roll bar, completely stock engine other than exhaust. and i was catching up to GTR's, corvettes, porsches, etc.. around corners and twisty sections, and pulled away from multiple sti's, because my cornering speed was fast enough that their straight line speed couldnt make up the difference.
fuck power for your first track car, dont even think of doing some kind of turbo setup or anything, you will last one track day, then end up spending the rest of your time pouring money into it. if your getting into track stuff for the straight line speed you are looking at the wrong thing. go to a drag strip if you want to use power to make up for skill.