Regular and Elite sounds like the best option. Breaking the level 100 cap is kind of a neat idea, but given the lack of a good reference or comparison in the real game it'd probably be a fairly major headache to figure out actual power levels and such.

Depending on how the system plays out, I might suggest some kind of perk or extra prize if a trainer manages to beat all the gyms' Elite teams. Nothing major, basically just something sort of shiny for the character to show off at parties or whatever.