I put new tires on before my track day and they were good. But I just melted them from side to side, the whole surface was just slagged. They're good tires, but after it started to rain, then I realized they were a lot harder than they should have been, which I attribute to their prior heat treatment. It took a thousand more mile after that to get the good grip back.
I guess my advise is to just use your old tires. Because if your melting them to the pavement, just about any tire will be good enough for the first time at least. If your old tires are already pretty trashed, perfect.
The track is a pretty nasty, exhaust environment. By the days end, it will have permeated you through and through. Get lots of good food and rest before and after.