I've got an 82 auto. As for engine swaps with the auto, forget it. Anything over 175 horsepower will tear the stock auto to shreds eventually. The adivce I got was to either convert to a W-58 maunal or retrofit the MKIII supra auto to fit wich can handle around 250-280hp approx. (yes, it's probably expnesive but not as bad as getting a rebuilt auto for the 82, my remanufactured trans cost $2800. The lowest bid I got was for $1500 and that was to rebuild the trans that was in the car that had only 1st gear left when I drove it to the shop. ;-) One to many peel outs!) If I had to chose again, I'd probably got the w-58, it's good up to around 300hp I think? If you can drive stick or are willing to learn, go with the W-58, it's alot more fun to drive with a manual anyway.
Your best bet is to make sure you get an auto box with whatever engine you plan to swap. The Mk2 auto shifter can easily be adapted for the auto boxes that come with the 7MGTE, 1GGTE, 1JZGTE, and even 2JZGTE!
Then sell your Mk2 auto box (sans shifter) to recoup some of the engine swap costs. If you can find a buyer (Maybe an old Soarer, Crown or Cressida owner?) - they are worth some money! The previous owner of my car spent around $1,300 AUD getting the auto reconditioned. And it is still crappy (as it was from factory). They can't hold much power, shift waaay too soon and are poorly geared.
But if you're planning an engine swap - sticking with auto (rather than going W-5X) is a lot cheaper.
JZA-61 in production
PS:Working in the alcohol and drug field, all my collegues get a kick out of the fact that my car has an OD button!