Instead of skillsets that allow skills to be aquired for less exp and retain them after death, Backgrounds would provide one or two passive buffs right off the bat that your character might recall from their pre-apoc life. Keep in mind these are just concepts and some features listed may not even exist in 4.0.
Police - restrain and search the inventories of other players faster because of your service on the local force.
Farmer - You can forage natural plants that nobody else can, due to increased agricultural knowledge.
Firefighter - Increase to damage done with Axes, and an increase to ladder climbing speed.
Soldier - Decreased recoil and gun sway.
Pilot - Increased aircraft speed and handling.
Fisher - Increase to boat speed/handling and a greater chance of a better catch.
Racer - Greater land vehicle speed and handling.
Medic - Bonus healing to yourself and others as well as an extra charge for multi-use medical items.
Civilian (default) - no buffs.
Track Star - Increase to running and walking speed as well as an increase to stamina.
Diver - Swim faster and stay underwater for longer.
These would hopefully encourage team play by making everyone specialise in a certain area rather than a single player acting as a Jack of all trades.