Alright, due to the hurricane I can't actually WORK on the car, but I can order parts!
I spent a ton of time researching wheels and tires. The Vair design limits tire and wheel size, so finding a good performing combo isn't as easy as other cars. I decided to go with a set of 15x7 Basset DOT-approved racing wheels, which will work both on the street and track. They'll also allow me to compete in certain classes that require a DOT wheel.
http://www.bassettwheel.com/dot.html
For tires, I went with Dunlop Direzza Sport Z1 Star Spec. They're one of the only 205/50/15 tires that have positive reviews, and luckily they have some of the best reviews I've found for a performance summer tire short of R-compounds. I guess I'll find out!
I went with a shorter sidewall than stock (stock is /70 I believe) because the car is and will remain lowered (though with new suspension), so there's not much room to work with. It'll also help out with steering response a bit. I also picked up a new set of wheel studs, longer than stock, and a set of chamfered lugnuts which are needed for the Basset wheels.
This is a project that I'll be driving while I work on, so I'll probably get these mounted, drive it for a week, and then start on the suspension.