OMG!? you gonna spend 5K on a motor!?.... you are one lucky bastard or a hard earner and have nothing else to spend on!!
well you have couple of choices for your AE86.
usually most commonly used are the 4AGE families...
4AGE bluetop, redtop
20V 4AGE silvertop, Blacktop.
Boosted: Supercharger 4AGZE.
and depanding on what your AE86 is gonna be used for (circuit, drag, street etc etc) the engine of choice is different...
check the master corolla forum for links and info, i canot tell you everything i know

but i gave you and idea....BTW i probably will only spend 2K at most for swapping...for my AE92 that is...