$15k would go pretty far towards a naturally-aspirated track day build.
You should buy a Sport Package equipped 370Z. You can find plenty with relatively low mileage around your target price of $25k. You might even be able to come in under budget depending on how many features you want (i.e. Base vs. Touring).
Add an oil cooler. You'll want one for track use. 25 row or higher.
Upgrade the brake pads to ones suited for track use. Stock won't cut it if you've got any bit of speed in you. Use DOT 4 racing brake fluid. You'll boil stock fluid.
Change the engine oil, transmission, and diff fluids since you don't know the maintenance history.
Check the tires. What the previous owner put on will depend on whether or not you want to run them on the track. Plenty of tire information available here.
Now that you've done all of that basic maintenance and made the car track ready, get out there and get a feel for the car as it is set up from the factory. Depending on your level of experience your first time out may let you know what areas you want to work on the most with your build.
Remember, you can mod all you want, but the most critical piece of the puzzle is
you. There is evidence all over enthusiast forums, this one included, where amateur drivers in heavily modified cars are significantly slower around the same track as a professional or experienced driver in a
stock car.
