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10mm pistol works well until you can fill out your armory.

Hunting Rifles are common and have some decent stats for early on

Beyond that, keep searching. My personal all time most used guns are

1. Chinese Assault Rifle 2. Combat Shotgun 3. 10mm Submachine Gun 4. Hunting Rifle The alien bkaster is technicaly an early on weapon since it is always in one spot. You don't have to do any quests or anything. It can be found north of the MDPL 13 Power depot. When you find it it will do 50-60 damage depending on condtion.