Holy crap, its finally my time to shine baby!!!
Haha, I happen to know more than common knowledge about supras.. Used to own one, my dad did too.
OK heres the basic layout my friend.
1986.5-1992 was the MKIII. In the US, they had the 3.0 Liter 7M-GE Engine, or from 1987-1992, you could spend a little more and get the turbocharged version putting out 30 more horses. In Japan, the engine used was a 2.5 Liter 1JZ-GTTE, a twin turbo but smaller displacement engine.
In 1993, Toyota introduced the 2JZ Platform in the MKIV supra. The NA model put out 220 horse power while the TT version boasted 320.
Basically, if your planning a swap, here's what you want.
Get a 2JZ-G(TT)E. If your looking for BIG power, then get a single turbo setup. As I'm sure everybody knows, supras make HUGE power on big single turbo setups, and if built properly, don't suffer enormous lag. If looking for a streetable fast car, going BPU with the stock twins will suffice.
Lastly, if your on a tight budget, you can buy a 1JZ-GTTE and swap the bottom end out with a 2JZ, forming what is known as a 1.5 JZ. It bolts right in. Using a 2JZ bottom end with the 1JZ components allows an extra 500cc of displacement, and the 1JZ's head flows much better then the 2JZ's.. Its a very common upgrade in the MKIII world.
For more help, allow me to redirect you to my former forum.
http://www.supramania.com
Any other questions feel free to ask.