The transmission issue has been solved for a while, just don't buy the first model year.
The Z06's can be bought in the $30k's depending on year and miles but you'd want one in the $40k's. The GT-R's are a bit more but worth it IMO. Go drive them both and decide for yourself. You are talking basic mods on both and they are in the 9's. Then again, Nissan offers a program to upgrade the GT-R to 2012 specs, so that's an option since you aren't buying new....
Either would be great but in TX you see Z06's everywhere so the GT-R is more rare but they are becoming more popular, not sure about OH...