Tires:  The most significant improvement to the car’s autocross performance so car comes as a result of new rubber.  Shod with Kumho V-710s, the car is several seconds quicker than with street tires mounted.  A second set of stock rims allows easy swapping. Update:  I have now gone through a set of these.  They have a pretty decent life span for a DOT slick.  I made it through a full season of autocross including a school a track day, and halfway through a second school before I finally corded one of the fronts.                           +  Ridiculous levels of grip             -   not cheap     *Edit:  I stand corrected. The exceptionally grippy compound of the Kumho V-710 easily trumps the water channelling capability of a street tire in even very wet conditions.  Standing water proves the only exception.
Sway Bar:  Stock class rules allow a front sway bar of unrestricted size as long as it can use stock mounting points.  I opted for a readily available Suspension Techniques bar.  It keeps the front of the car noticeably flatter through tight corners.             +  Less body roll             +  Better steering response             -  Can break mounting tabs on MR2
Air Filter:  I opted for a K&N reusable air filter.  Rules allow swapping air filters as long as the new one fits in the stock location (In other words, no converting a panel filter to a cone).  One can only expect modest gains from such an upgrade, but any little thing can help, especially when so simple.               +  Reusable/HP gain             -  Must clean often
Driver:  With the possible exception of tires, the largest improvement that an average driver can make towards improving run times comes from improving their skills.  To that end, and keeping in mind future competition potential, I attend as many driving schools as time and money allow.   So far: CarGuys  -Shenandoah Circuit @ Summit Point NASA HPDE 1  x2 -Carolina Motorsports Park -Road Atlanta ETR SCCA Autocross School x2
More Tires:  No longer focusing purely on autocross, and planning to make a few trips to the track this year and next, I decided to invest in some dedicated track rubber.  The Toyo R888s have far more grip and a more performance-oriented design than the street tires, but have a far longer life expectancy than the V710s.  Plus I don't use up the expensive V710s running them at the track.  OEM wheels for the MR2 are a dime-a-dozen (I should know, I have a dozen ;) )                         +  Fun Grip             +  Can handle standing water             +  Longer life than V710
Harness:  Going into an off camber turn and coming out of it with the seat bolster lodged firmly between your butt cheeks is no fun, and also very distracting from the whole "driving" thing.  I solved this problem by installing a harness bar and 5-point harness set up.  It is not installed to exacting road-race specification, but is safe enough for autocross and track-day use.  If I get more serious I will really need racing seats that allow the submarine belt to be properly mounted.                         +  No seat-bolster wedgie             +  Allows you to concentrate more on what the car is                 doing and less on where your ass might be going.              -  Slower to get on/off than a normal belt             -  Will make you look like a tool if worn away from the                 track/autocross
Extinguisher:  This is pretty self explanatory.  A fire extinguisher should be securely mounted within reach of either occupant.                         +  Because being on fire sucks