Balance is everything - which isn't to say that not spinning the wheels is the ultimate goal! It's fun yes, but the proper balance is driving the curves and how it handles. Old hard tires or sticky racing slicks won't change the "characteristics," just the break and controllability.
By balance we're talking about how it handles in a perfect neutral power 4 wheel drift. Yes you're in the corner at the maximum speed, it you lift your foot off the gas the back end comes loose. If you push down on the power the front end will drift a little. This allows you to steer with throttle!
Soft sticky tires allow you to explore that region and maintain control more than mileage tires or old hard ones, but either way it's all about how the car is balanced.
I have a narrow body car with old 215/60 x 15's on 7" wheels on the back and I do have to feather the gas a bit in 2nd, but other than that it just locks up the 330 or so HP and it goes. I'm running 200lb springs on the back and stock sway bars all the way around.
Click to view attachmentmy rear springs tested out at 208 and 211 lbs.
Click to view attachmentThose are 215/60x15 all the way around with 15x6 up front and 15x7 on the rear. Actually a hard size to come by anymore.