OP, the beginning is usually the hard part to survive in the game, because usually, ya don't start out with a gun!
As mention earlier, 10mm pistol can be found in a rat nest in the trapper section. Oh, and don't worry about conserving ammo. Ya ganna get ALOT more ammo and handful of weaponry from the Den and from there on.
I forget his name but there is a guy in the bar in Klamath that'll train you in either unarmed or melee (don't remember which...maybe both) if you buy him a drink
His name John Sullivan. He teaches pugilism.
And do you think I should tell him how to get the Enclave power armor early?
Kind of kill the experience, in my opinion.