If you don't play Champions then you're basically just playing normal pubs with the possibility of better people. Most of the time, competition in TDM and Moshpit is just as lacking as public matches. The system was designed around playing the Champions series with a party of 4, so that's the best way to enjoy League Play.
As far as the classes that people use - it depends on their skill level. Most of the better players will stick to the same classes that they use in tournaments.
Oh, and by the way, I win again :D