Modern day survival is about staying employed and paying the bills. But what the heck, I'll play.
I'll assume you mean out the woods-type survival, because of a riot or natural disaster. I don't know how any intelligent person can even mention zombies. They've been watching too much TV and losing their grasp on reality.
Taking and maintaining a pump, spare seals, tools to work on it all.... now, we're out of the reality of survival. If we have that kind of tools and equipment around, we may as well just have a 22 rimfire and a few bricks of ammo. (subsonic, if you want to be quiet) Maybe a Marlin 39A.
But OK, assuming it HAS to be an airgun, and a realistic one for survival, I think I would go with a quality springer. No PCP because of the seal and support gear issues. Something that can go many thousands of cycles with no maintenance, and work in the cold too. I think I would go with a tuned Diana 48 Panther in .22, and probably a fixed high-end Hawke 4-12x50 scope with the lit reticle. Add a shotgun sling and as many Air Arms domes and Baracuda Hunters as I can get. It would be tuned with minimal tar/grease, so the performance would stay pretty constant as outdoor temperatures shift.
I figure with a 20 FPE .22, I could take all small game easily out to 30 or 40 yards. Since I'd be in a survival situation, I also wouldn't hesitate to take head or neck shots on large game. I don't care if it takes them awhile to bleed out; I've got all the time in the world to track them down. Also, since I only have one gun (and again, lots of time) I presume I would get REALLY good with it. I think I would first go after squirrels, coyote, rabbit, possum and raccoon. Any kind of bird, when the opportunity presents itself.
I figure that rig looks scary enough I could use it to defend myself through intimidation, if needed. If that fails, take a shot and run!
The pumper idea that oldspook mentioned is a good one too; only problem is that a lack of a good way to mount a scope pretty much limits its range. An aperture sight is a thought, but that only gets you so maybe 30 yards. I want to be able to make head shots on deer at 50 yards. A tuned Sheridan Blue Streak would certainly be an easier rig to carry around than my D48 beast, but also somewhat less capable.