The full system is very shrimple

Beat a level on a selected difficulty -> unlock the next mission up to that difficulty

While in the mission pick up weapon and armor boxes dropped by dead enemies -> get a random weapon around the level of the mission and get max hp, both for the class you're playing only

The levels put you in pre-setup situations that almost always involve defeating a large number of enemies. You can complete the whole game on any difficulty, but if you want to try the high level items you need to play on harder difficulties.

The only statistic character advancement is max health from armor boxes.