Don't forget sub-classes such as Paladins. Paladins in my opinion, are the most expensive classes to level up. They have good m/s and h/s at max level though, so not so costly then.

Birds often do not take aggro, so they don't spend much on health potions.

As for the richest class - It is between mages and birds. Birds are a definate for bosses, so many people with birds boss farm a lot. Which means lots of rare item drops. Enchantress's are the big badies when it comes to steady cash. The best run of gold I ever had in Plasma Pyramid was 12.5k gold and a 15k boss drop. But like I said, that was my best. A Enchantress pulls in 2-6k gold on average per round of plasma pyramid.