The game contains four classes: Gunner, Arcanist, Channeler and Warder.
Gunners are proof that anyone and anybody can effectively learn to fight. With their wide variety of attacks, from fire to chem, they can fully destroy most enemies from range. The Gunner is a ranged DPS class notable for their use of projectile weaponry.
Once, only few could use the magics the arcanists wield, but with the advent of mass produced staves, many can now use magic to great affect.
Arcanists have very powerful spells, but given the recast times of many of them, and the steam costs, it is a difficult class to solo with, and would be best teamed up with a Warder or a Channeler. They also have some of the coolest graphics and each tree has a nice balance of skills.
The Warder is a melee and defensive class.
Another trickier class to play, especially when you get mobs who run around (thieves!!). They have decent solo ability because of their durability, and while their damage isn't the greatest, they get an excellent array of buffs to augment your group. I do think that if someone was going to go down the buffing line they need to have a bit more damaging skills available. I would also like to see them have buffs that would stay on but take a set amount of steam from the steam pool.
The Channelers have found that the world machine makes sounds, such as when it heals itself. By sychonizing and imitating these sounds they have found that they can produce wonders. The different trees are very fun, and (so long as you have the healing skill upgraded a bit) can solo with any tree quite decently. I would also like to see them able to have persistent buffs up that reduce the amount of steam in your pool. This is a very versatile class that (at its current stage) needs little work done.
Overall I think the biggest thing with any of the classes is managing your steam usage. It is very important to get out of combat after you kill something (which is a bit of a pain in the butt with its current right-click toggle). It would be great if after mobs are killed, and if there are none on their way to attack you, you automatically went out of combat.
Potions aren't too expensive, but all of the classes will rely on them if you want to make your way through dungeons at a decent pace, especially with the combat having to be manually disengaged...