I pick the Gunception rifle,
or failing that a Kaltec KSG 12 Gauge with 14 round dual ammo tubes plus one in the chamber. with like a duffel bag full of flechete rounds. 8-|
Melee: A Space Marine Chainsword
Seriously, what zombie apocalypse is complete without a gut-ripping chainsaw? And what's better than a chainsaw? A ChainSWORD.
Vehicle:
A WW2 German Zuendapp KS750
Although not as powerful as some of the newer motorcycles. It has that awesome vintage look. Strap my crossbow onto the sidecar, place a friend in the side car, one hand on the wheel, the other wielding my chainsword, ready to strike down zombies at 100 km/h, and we've got a zombie death machine.
I also have 2 AKs, a heavy FNFAL, SVD, and a bunch of other stuff with about 5k round of ammo. The truck is a multi-fuel so it will run on literally anything that burns. So after I flatten a hoard of zombies with it I can cook them for the fat oil and go another 300 miles.