1. Alakazam - turbo-smart so he can help me solve any problems. He's an incredibly powerful psychic, too, and certainly able to detect any approaching zombies. His telekinesis would probably make him strong enough to repel/destroy any zombies all by his lonesome. No zombie is getting past this guy. With the vastness of his psychic powers, he can really do it all. Teleportation, Barriers, Disabling attacks, Mimicking any other ability, can attack in its sleep, can reflect select moves back at opponents, and has access to all elemental punches. Catching fish? Please, he can pull them all out of the water at once if he wants. Any issues with angry zombies or other trainers? He can control minds. Totally hax. MVP!
2. Politoed - water. Drizzle means I can have rain whenever I want. Can swim.
3. Tropius - unlimited bananas! Strong, large, and can likely help with shelter-building.
4. Hydreigon - personal bodyguard (in the event that Alakazam for whatever unforeseeable reason can't handle a threat) and transport. Powerful all around and can levitate, which is as good as flying. Three heads = firing three blasts at a time, killing untold numbers of zombies, all while levitating me safely out of zombie range. Has access to Fire Fang to set shit on fire.
5. Pachirisu - Its ability PickUp makes it a great scavenger, able to find all kinds of useful items and berries, which can then be planted or eaten. Also electricity.
Granted, you said you "have" no items, but this Pokemon has an ability which allows it to find items others don't notice. If this one doesn't count, I can easily find a replacement.
6. Blissey - with moves like Heal Bell, Aromatherapy, Heal Pulse, and Softboiled, she is our backup in case of infection and an obviously indispensable team member--it's not surprise she's popular on this thread's lists. She's can also sing to put enemies to sleep, has access to elemental moves such as fire, ice, and electric moves, and can attack in her sleep with Snore.