My brother and I went last year in our 66 belvedere I.
To answer your tire question I would recommend both street and race tires. We got by on ET Streets but when it rained(STORMED) we had to pull off at the next exit or the side of the road and that just kills more time on the road that you probably don't have to waste. Its the one thing I would take if we do it again.
Other than that cooling system parts and a cooler full of cold water are the most important.
Its a rewarding adventure but also punishing if its hot and it usually is.
Good luck, Bryan