[psgvaint] Classification of classification of finite simple groups

The giant proof has many parts.  "Outside" the known groups is the proof that no other finite simple groups exist, i.e., the giant proof is exhaustive.  Then, for each known group, proofs of existence, uniqueness, finiteness, simpleness.

Pedagogically, one could present these parts in order from easiest to most difficult.  Which parts are the easiest?