Cop isn't bad, but it can be difficult once you blow through your starting ammo. On the plus side, you pay the Civilian cost for all skills, so it's easy enough for you to grab anything instead of having to build up in either Military or Scientist first.
Grab Free Running like Dev said. The way it works is, normally you can't enter any building that's barricaded heavily or higher. With Free Running, you still can't go in the front door, but you can enter from the inside of an adjacent building regardless of barricades.
Pick up Construction quickly as well, so you can barricade buildings. There's no XP in it, but it can help keep you and others with you alive.
For early leveling, good ways to gain XP are combat using a fire axe (lower damage than your gun, and lower accuracy when the Pistol skills are maxed out, but no downtime searching for ammo), healing others like Dev said - Diagnosis lets you see who's injured so you don't waste AP trying to heal random people. However, if you're hanging out in a well-occupied hospital, odds are the people in there will say when they're injured to give you a chance to heal them for XP.
Items you'll want and where to get them: Fire Axe (Fire Station, Warehouse, Auto Repair Shop - best bet is a Fire Station
Flak Jacket (as a Cop, you should have started with one - don't drop it. It'll help protect you from PKers.)
Radio (Again, you started with one. This is mostly just useful for hearing broadcasts from other players. Over at Tarasius Hospital in Lerwill Heights, where most of us are, we broadcast on 27.77)
First-Aid Kits (Hospital. Use to heal yourself and others. Try to keep at least one on you at all times in case you get infected)
Once you get Construction, try to get a Toolbox so you can repair ruined buildings (ruined buildings are a darker gray than other buildings. A ruined building cannot be be entered via Free Running, it will dump you outside and possibly injure you).
If you're hanging with other players in a safehouse and zombies attack, protocol depends on how many get inside and what your skills are. Until you get Construction, obviously focus on either killing and dumping the zed ASAP or healing whoever is being actively attacked. Once you get Construction, if there's only one zed inside - barricade the building back up first to prevent more zeds from entering. If there's more than one, this gets difficult because the more zeds there are, the harder it is to barricade the building.
If you do get killed and become a zombie, don't panic. It's simple enough to get revived - head to the nearest cemetery or *outside* a church, or the local designated revive point if there is one (Bragg Park where we are), and simply wait to be revived.
When you gain the capability to revive others via the NecroTech skills, remember one thing: DO NOT COMBAT REVIVE. What this means is, while it may seem easier to revive an attacking zed than to kill them, this rarely ends well. Many zed players *like* being zeds and will react poorly to being revived, often using whatever weapons they've been carrying and unable to use to attack survivors, free run into a building when as zeds they couldn't. etc.
Once you have your Axe Training skill and the other essentials and are comfortable gaining XP, you may want to start setting aside some XP for zed skills. Lurching Gait and Ankle Grab will make being killed, rising as a zed, and moving to the revive point cost a lot less AP and thus remove a lot of the hassle. Other zed skills are optional, but I'd focus on the survivor ones first, and don't pick up Brain Rot unless you decide you want to play as a zed instead of a survivor - in which case, get off the thread and stop spying on us.
Any specific questions, let me know.
Oh - and don't search in random buildings, it's usually a waste of AP. Use the Wiki to find out what buildings have the items you want.
Map of the city:
http://map.aypok.co.uk/index.php