Try a melee character. It's a little hard in the beginning, working with knives and lead pipes, but as you progress it becomes more and more fun. When you can, get a Fire Axe. That one never gets old. Charging at some chump stuffing his face at a table, doing this awesome spin attack right into him... Man, what a weapon. My current character is a little sadistic xD
Bumper Swords, Chainsaws, Nailboards and Rebar Clubs are also great. Oh, and get the "Oh, Baby!" from the cave near Jacobstown. Get your Strength up to 10 though. Anyway, I always used to use guns only, but Melee weapons are surprisingly strong once you've put some points into it. I usually take out light or medium-armored people down with my Fire Axe in one "charged" hit.
Happy hunting