State of Decay: Year-One

If you are working on completing all the achievements in the game, you will likely complete the Wilkerson family quest line... once you've done this, an M60 automatic machine gun is unlocked at their enclave. It costs around 170 influence to grab, but it can hold 100 bullets. You can also attach a suppressor, if you desire.

If you're in a home base that allows you to upgrade your watch tower to a shooting platform, you can spend 3 ammo resources to start shooting training, which greatly increases your experience earned from shooting. With the M60 and the experience buff, I was able to go from level 4 shooting to level 7 shooting by driving around and finding hordes of zombies. I'd attract their attention, hop out of my car and mow them all down. I only had to do this about 4 or 5 times to max out my skill.