Question: Are we excluding game elements such as command prompts, menus, item storage, etc... ? What about ammunition? For example: If I roll with a BFG 9000, will I be able to replenish the ammo or am I cooked once the ammo runs dry?
If this is one of those "No video game mechanics apply. You get a *single* item to use in the real world, which may or may not be effective in your hands, so chose wisely" situations, then I'd probably roll with the following:
The Infinity Pistol - Borderlands 2
Given the circumstances, it's the best weapon I can come up with for now. It has a good fire rate. Its relatively compact. Easy to use. Never runs out of ammo nor does it overheat. It may not be strong enough to handle all of Pandora's badass creatures and mutated enemies (without the help of other gear), but it should be more than enough to stop the living dead. Plus it gives you the opportunity to keep at least some distance between you and the threat. AND you can get it with elemental rounds, such as fire.