At the risk of over simplification: fit the widest stickiest tires you can for pure grip. The too much power for a light car kinda doesn't really hold water for me.................Brabham BT45 (I think) F1 car, 1200lbs and 1200 horsepower in qualifying trim didn't have this issue becuase it features massive slicks that were up to temp, a street car is not going to have heat in the tires at a level you get at the track...................which brings me to why I don't get the whole street racing thing. Dirty tarmac cold tires etc.................what's the point.
Now you can optimize the suspension and run the best tire possible. There are all sorts of things you can do with damper setting and suspension geometry and tire pressures etc to get more out of a car etc. The notion that a light car can have to much power is silly..........................focus on getting the power to the ground, if you don't want to run the best set up for this, then yes wheel spin is going to be a by product.