[strat61caster]

Changing tires won't fix your handling problems, at best it will mask the problems by adding enough grip that you're not driving at the limit of the grip available so your times improve and everything feels great, until someone steps in behind the wheel actually drives it at the limit, or you step up your game and the problems return. At worst it could actually exacerbate the problem, especially as the tires wear in an imbalanced fashion.

What classing and ruleset are you building to? This can be extremely restrictive to your wheel and tire choice and buying what you want without looking will put you into a class where you will be noncompetitive unless you spend $5k, $10k, $25k on modifications adding more lightness, power, and grip.

If you're just doing it for fun, awesome! Do what you want.

My 2 cents are, again, tires won't solve anything. From a stock setup the thing most lacking is camber on the front end. Adding camber up front will add grip on the front tires when turning reducing understeer, camber bolts will put you in the -1 to -1.5 degree range, a big improvement over stock which is usually less than -0.5 and perfectly streetable. With bolts and camber plates you can run up over -3.0 degrees which felt great for me, what you do will depend on the class you want to run in.

The two most common classes for autocrossing an 86 are SCCA CS and STX. With CS you are limited to OE size wheels and OE crash bolts, STX opens up a lot of possibilities but you're looking at around $5k to get in the ballpark in terms of tire, suspension and power and some real talent to get it dialed in.