Basically, some years ago, modders ripped apart the game and threw out all the dummy data and other unnecessary things for optimization. That's the Mini version. And the one most mods made today depend on. So, get that one.
Artificial Academy Unlimited is a mod that depends on the Mini version. It massively expands the number of sliders, traits, personalities, outfits, and other things the game can do. (Most of it inside its own separate menu, like all the new sliders being in a pop-up instead of the normal sliders tab.)
AAU also adds a new mechanic called Modules, which are basically traits with more complex or specific functionality and many of them completely change the way characters behave even with just one module on them. Or add whole new mechanics like the Detective module does.
For any other questions, you can find answers to them on the wiki linked in the OP.