IMO, for the kind of open track day you are looking at, you don't need an exclusively built track car. Take whatever you have now and drive it. Good tires, good brakes, basic safety and working seat belts are all you need for this type of activity. Heck, even a daily driver can do this in a lot of instances. There is absolutely no reason to build a track day specific car if you desire is to simply turn laps. Once you try it and see if its something you want to continue with, then you can evaluate activity specific vehicle builds.

Drag racing has really dialed this in with E.T. brackets. The road course and cone bashers haven't done as good a job of getting this message out.