Explore, explore, explore.. There's tons of stuff not related to mission/quests/story out there for you to find. Lots and lots of places and enemies to loot. They aren't marked on your compass so you just have to go out there into the wilds. You can explore all of zone 1 without having much worry because it's a low level zone.
In the beginning, even if you want to eventually use automatic weapons, it's better to conserve ammo with single shot weapons. A hard hitting shotgun blast is much better than a low damage bullet spray when it comes to conservation. Wait until you start finding or crafting better damaging weapons to start using automatics.