Well, Hoosiers makes racing AND auto-x tires. Make sure you get the right compound. A racing tire will not heat up quick enough in an auto-x to be effective as compared to the purposely softer auto-x compounds. Vice-versa an auto-x specific tire will heat up to fast and suck in a higher speed track environment.
Remember with 'competetion tires' it will put you into a different class....most likely a tougher class to be competetive in with that car. And even with slicks...you probably are not going to keep up with any of the 'smaller cars'. As for brakes...they aren't so critical in auto-xes, some folks (like me) might say not to use them at all if possible while on course. Spend your money elsewhere....like lowering springs, sportier shocks, upgraded sway bars and bushings, etc..
Take a look at Falkens ST-615s which are high performance tires with very stiff sidewall characteristics. They will keep you in a street tire class. Also a favorite tire among the SCCA Solo I crowd in the STS classes. Just don't drive them in the rain ! Just my 2 cents ...and over 100 auto-xes under me belt.