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Big difference between road race and autocross.



I agree with this. Autocross emphasizes high levels of roll resistance which can come with high spring rates and big sway bars and a lot of shock control to manage it all. Road race will want slightly softer spring set ups to allow suspension compliance with the road and higher sway bar rates to resist roll and will need more mucho more brake than autocross.

If you've done autocross before, you're already somewhat familir with it, but classing systems likely have changed. With an AlterK under the car, you may find yourself in a catagory where you are uncompetitive to the level of prep other cars have in the same class. If you're just going for fun to see what you can run, this is no big deal. If you actually want to win, then you may find you need to continue to modify the car to be competitive. http://www.rmsolo.org/ for more info.

Open track days at HPR are non-competetive. You can run against the clock and have gentlemen agreements with other racers, but it is not wheel to wheel, all out efforts. As such, I wouldn't worry to much about maximizing your car for it until you've put some time under your belt. If competition is your goal, I'd also second the suggestion to start out with NASA HPDE and a detailed read of the rule book. Work your way through this program to get a feel for the environment. Once complete, you can look at whether you want to run in their Time Trials program or a wheel to wheel racing program such as American iron. NASA Rocky Mtn runs at HPR, PMI, and PPIR locally with trips to Texas and Utah on occasion.
http://www.nasarockymountain.com/ for more detail

To get started, I'd swap out the drag rubber for something with less sidewall, maybe some 17x8 with at least a 255/45, 200 treadwear rating, turn some laps, and see what you need to do next based on where you want to go.