Resurrecting (LOLZ) this topic to appeal for more players and suggest the formation of an in-game group. Everyone and his mother has a group of teammates, and I want in on the cooperative action, dagnabbit. If we have a friendly group of people we can coordinate our efforts, get healed/revived when we need it, etc.
To answer questions:
Soldiers and policemen - firearms-oriented combat characters - should seek out Police Departments, where can be found flak jackets, pistols, shotguns, and ammunition for both. Their role is to kill zombies.
Firement and other melee-oriented combat characters should grab a fireaxe from the nearest Fire Station and set about merrily hacking away at the undead.
Medics gain five XP whenever they heal somebody. Medkits for this purpose can be found in Hospitals, which is also where people go to get healed if they need it.
Scientists have two main routes to gaining XP. Firstly, using their DNA Extractor on zombies (each zombie can be tagged once a day) gets 5XP a shot. When they gain the Lab Experience skill, they can use Necrotech Syringes (found in Necrotech buildings) to turn zombies back into humans.
Any character can perform any of these roles by buying the relevant skills.
Careful where you sleep. Zombies will check Hospitals and Police Departments regularly (especially the former, whose occupants often cannot defend themselves very well). Unless you're in a safehouse (a barricaded building with lots of survivors), don't spend the night in popular and noticeable buildings.
Stay out of Shearbank. The suburb of Shearbank has been taken over by a group of survivors calling themselves DARIS (the Democratic Armed Republic of Independent Suburbs). They will kill anybody they find trespassing in Shearbank.
Useful links:
Map of the cityForumsFAQZombie Tracker