There are advantages to each, and of course disadvantages.
The advantages I could go on, and on, and then some...
It really comes down to your personal choice.
I will try and help some by giving the more common issues with each.
They are both great choices, you really can't go wrong with either one.
MKI
Avoid 1985 model. The 86-89 models have much better upgrades. Of course you can put the upgrades onto the 85 model...
Avoid power windows, they are doomed to fail.
The dizzy is in a bad spot, making it harder to work on.
The battery is in a bad spot, next to the engine, you can move it...
MKII
Turbo, Non - Turbo? This will make quite a difference in the price of the car.
91, think 92 as well, has speedo issues, mechanical cable.
Get a carfax, it can help if the car has really low mileage.
91 has airbag recall, check this out at dealer to make sure it has been done by getting the vin #.
91 has issues with drivers side door wiring. I have found the drivers side speaker rarely works in this year model. Easy fix, run a new wire to the speaker, and replace the speaker while at it.
Power antennea, few work...
Valve cover gasket, seems to be common, very easy to fix, but usually not fixed, which ends up leaking oil all over the engine, making it harder to find the leak, then covers fuel rail in gunk. Can all be cleaned off. Can also be used as a neg. to get the seller/dealer to lower price of car.
Power steering? I don't like it on such a light car, but think it can be pulled out without too much trouble, my opinion only, hunt for MKII without p/s.
All of these are minor issues, but most people who own cars just drive them, and will not put any money into them. MR2 owner, who owns the car, not making payments is the exception.
You mentioned autocross, I was going to mention you should expect to invest in some things right away. Struts, brakes/rotors, wheels/tires, and.... if you do nothing else, replace the timing belt, unless you plan on replacing/rebuilding the engine.
Happy Hunting