You could probably handle a fighter character as well. Not as hidden as the evil characters, but not as obvious as the priest, either
Nobody would be able to physically take him early on, but his power growth would fade into the others over time. (Priest would have trouble getting his followers to attack a 'law abiding' citizen, demonologist and thief are busy with power building.)
Power buildup could be on a (unique) xp system, building power killing the red herring thieves and cultists
Actually, you could possibly add supes to this. A Vampire would be a good example for the fighter class (Power by eating people OR turning them into mind-slaves), and Werewolves could be in the business of creating (biting) new werewolves. (Which wouldn't be controlled, but keep the city guard occupied by being A-rank NPCs)
Slaves: Either expand vision (mindlink) or serve as fighters. Imagine turning the priest's guard? Except the church would serve as protection from the Vamps, their servants, and likely the demonologists...
Ritual is important to a game like this. In order to 'blend in' and make investigation useful, players should be required to do things at certain times.
Priests should be required to hold mass at regular intervals. Your opponents will know where you are, but you are in your stronghold, surrounded by your full minion strength. This allows people to plan their attacks accordingly.
Demonologists could be bound to their summoning circles. Their play being to go get stuff and come back in order to do a ritual to get the full benefit.
Thieves... would need to visit fences (money buys consumables, elite gear must be stolen?)
All three should need to eat occasionally. (This simulates a brief 20-30 seconds of vulnerability for the thief)
The supes would have patterns of feeding that lead to their exposure as well
I'm a big fan of subclasses:
Priest
Faith : Guard is on your side 100%, many weak followers, but you can't get them to do as much: Holy Powers involve defense and protection
Cult : Guard is on your side 50%, fewer followers, but they are more rabid, stronger, and will do more things for you, including less than legal things. Holy Powers involve strengthening followers and subverting city guards
Thief
Sneak : Hide in the shadows, pick locks
Brute : Protection Rackets and Bank Jobs. More visible, but you get power quicker (Also raises notoriety: chance NPCs will recognize you)
Arcanist
Demonologist : Powers from Hell. You get subtle demon buffs and powerful minions (Strength buffs, wings, + demon minions)
Necromancer : Powers from Death. You get massive personal buffs and weak minions. (Turn into a Lich, 1 Franky Golem, many skeletons and zombies)
Minimum players is a must. It's important that you don't move against the other players without exposing yourself (so at 3 players, if you jump at one, you're all out there for the other to strike you, plus you're likely exposed to the city.)