I often take a melee/guns hybrid character to deal with zombies at the start of my game, before I get any guns. Beyond window-camping and beating down the zombies with a crowbar, I never use melee, save in dire emergencies.
To get guns from stores early on while dealing minimally with zombies, I recommend just fleeting to the ammo shelf, and quickly 'e’xamine what types of ammo there are; you’ll undoubtedly find either .40, .45, 9mm, or some variant of shotgun ammo (or if you’re lucky, all of them). Rush over to the handgun or shotgun racks, take one or two of each, then grab the ammo for them. The shotgun(s) should clear you a path to a few stores for looting, and the pistol(s) to get you out.
This fleeting strategy usually works for me, generally with minimal damage taken. The most damage you’ll take is likely in the gun store itself.
This is, of course, in Static spawn mode.