Sticky tires have virtually nothing to do with brakes other than the fact that they can be used harder since the tires stick more. That is of course assuming you can use the new 'stick!!!!!' I've never had issues with brakes, AH or anything else relating to tires.
Best advice - turn the 'helper modes' off. AH or comp mode usually teach students very bad habits. A good driver can always beat the stock computer modes. Turn everything off and build your speed slowly. Keep with the basics: brake and shift in a straight line; slow in, fast out...be smooth. It's a Driver's EDUCATION event. Use it to teach the driver to be a better driver - not to let the car 'bail' him out or teach bad habits and wear out the brakes!!!!
As far as driving the Hoosiers. Don't slide the car around a lot. To get the fastest consistent lap times with the Hoosiers means using very slight slip angles. If you're dirt tracking the car around the corners, you'll be overusing the tires, the car and the driver. Drive smooth and keep the oversteer in check and you'll be fast. After you try those, then put on a set of the V710 Kumhos and go even faster...easier!