If you're just starting out, focus on making the car reliable and safe... the harness, seats, suspension, brake pads (get some racing pads like EBC Greenstuff or Hawk and upgrade to DOT4 fluid... eventually, you'll want braided lines, too... all of this is not just to make your car stop faster... it's to make sure your brakes still work after three or four laps).
Get decent tires, but don't go for R-Comps, yet... do everything else first. Going on racing rubber means you'll actually have to sort out the suspension completely, as a car that feels well buttoned-down on stock tires can feel like a bucking bronco on R-Comps... and it'll be just as dangerous, with unpredictable handling limits. Learn on some regular Hi-Po tires, and upgrade as you upgrade the car. Advan Neovas are great, but I've been hearing good things about Falken RT615s. You can use either of these tires on the way to and from the track, also... just take it easy, so they won't wear out. Neovas have good heat-resistance (in fact, the hotter they get, the faster they go), so they're a good tire for multiple laps.
I've been hearing good things about the new Federals, too... don't know if you can get them, but over here, Federal's R-Comps cost only as much as Neovas.
Note: with Neovas, you'll have to at least have new shocks and springs... ideally aftermarket. In fact, if the car is for track use only, invest in coil-overs with height and valving adjustment (which would help with rallies). My car went to a few track-outings on stock tires and did pretty well... but when I switched to Neovas, the rear end got a bit squirrely, because I had more grip than suspension composure, and the rear was rolling around on the tires... still had corner-grip... but that extra time waiting for the car to settle before going for the next turn or getting on the power will make you slower... had to upgrade due to that.
Other track-reliability upgrades would be to replace all the coolant hoses, as well as the radiator cap... check if the water pump still works or if it needs work... a set of gauges for oil pressure, oil temperature and water temperature are a good addition and will help you avoid a costly breakdown on track.