Dont get DOT legal R-comp's unless you know what are you are getting into (Pilot Sport Cups, R888, NT01, etc). They will grip while they last and havent heat-cycled out. They get expensive as they will only last for a few track days. They will not give you much warning when they break traction.
Extreme Performance tires for mere mortals is all you need. They offer plenty of grip, last up to a full season, and typically work pretty well on the street.
Dunlop Direzza ZII StarSpecs, Yokoham AD08R, are all good choices with stiff sidewalls. Not sure about the sidewall of the Bridgestone RE71R, but the tread pattern looks remarkingly similar to Dunlop ZII-SS. A few track members have used them and love them.
RE-71R:
ZII-SS
