TRD and Kaaz also make LSDs for the AE86.
As for the engine swap there are many options. I've heard of the mustang 5.0L being droped into a Corolla GT-S before. It all really depends on how much your willing to spend. The easiest replacement is the engine that was already in the car, the 4A-GE. Because it was the engine that came with the car little work is needed. Where as other engines may require custom work. More popular swaps seem to be the 4A-GZE (supercharged version of the 4A-GE) or a 20v 4A-GE. But it all really depends on your budget.
As for the engine swap there are many options. I've heard of the mustang 5.0L being droped into a Corolla GT-S before. It all really depends on how much your willing to spend. The easiest replacement is the engine that was already in the car, the 4A-GE. Because it was the engine that came with the car little work is needed. Where as other engines may require custom work. More popular swaps seem to be the 4A-GZE (supercharged version of the 4A-GE) or a 20v 4A-GE. But it all really depends on your budget.