Back in 2002 Chevy took the 02' Z06 and ran it for 24 hours on a race track. Now they didn't just start a clock and 24 hours later were done. They would start the stop watch only when the car was on the track and then stop it when it was off. A true 24 hours test.
I think if you have few, and I mean few, engine modifications, your car can be very reliable. You are going to have wear parts (tires, pads, rotors).
The rotors are easy. Just go to NAPA or Advanced Auto Parts and buy the cheap blank rotors. Dont spend a bunch of money on drilled and slotted Kryo frozen rotors. I know this sounds counterintuitive but any guy that tracks a car can tell you rotors don't have to be great to stop a car. It's the pads. Spend the money on the pads and your car will stop on a fricken dime. I have one word for you...(Carbotech)
Tires, well choose your posion. They do wear fast but if you take it easy you car get two or three good track days out of them. Nitto NT-05 are good but the NT-01's are better. $1100-$1200 per set.
Steel braided break lines are a good idea for safety. Your pads and rotors will get red hot and the heat can transfer to the rubber lines and possibly melt them.
Racing break fluid with a higher boiling point is also a really good idea. I use Super Blue.
Gas! Now why would I say gas? The government has mandated that a certain amount of gas stations in the united states carry Ethanol enriched gas. Unless you car is a Flex Fuel car don't use any gas with Ethanol in it. Here is a link to a site that shows all the non-ethanol gas statins in the US and Canada.
Hell there is even an App for your iPhone.
Good luck and have fun running the Z on the track. As you can tell by the posts it's not a cheap hobby. If you want cheap, buy a Miata.