I agree with Kopper! This is the type of question to which All Answers are Incredibly Wrong, simply because none of us has ever faced anything even remotely similar to the situation described. And worrying about "A Record" (ANY RECORD) would be completely unimaginable at the moment about which we're speaking. Thank goodness we don't have to face THIS in reality.
If pressed into it, though, I might could make a choice or two.
If it was the Desert Island thing... Screw the iPod. Throw it into the lagoon. Grab Ginger and Maryanne by the hair and drag them into your hut. There's no electricity here. Your iPod is alive for the next... what? Two Hours? Maybe?
Zombies are different, though. For one thing, they're not Intentionally Destructive of Anything Other Than Human Flesh, so Power Plants are going to continue to operate. Without an active, involved and ALIVE staff, however, a Coal Burning Power Plant won't last more than about 6 hours (maximum). If you're lucky enough to live within the range of a Nuclear Power Plant, you can probably count on it continuing to work for a few months. Regardless of how long it takes for it to die, You will want to stay the hell away from it for as long as, well..., EVER!
I would probably choose The Rolling Stones' "Exiles on Main Street", which sounds horribly lame and "Rolling Stone Magazine Influenced", but is the only record I can think of that contains all of the variety that I would need to survive a Zombie Holocaust. It caught The Glimmer Twins at their most creative and most messed up moment. It Proves that You Can Do Great Art Under the Influence! Well... Okay. Maybe not that YOU can, but that Someone Could! It's raw without trying or pretending. It Rocks, It Grooves (which could come in handy if there are any surviving females or if there aren't and you become horrifically desperate), and It Twangs. It's not perfect, but then... Neither is living in a Secure Structure in which you are surrounded by Flesh Eating, Formerly Living Friends, Neighbors and Family Members.
Lets face it. Zombies are Dead People. Dead People are made of Dead Flesh. Dead Flesh doesn't last forever. I figure I've got to spend a couple of months (at the most) listening to the same record over and over before the flies have chewed my mortal enemies to tiny bits. Then I can go to any record store I want and take anything I want (although, despite my Lifetime Supply of Makers Mark and Pabst Blue Ribbon, I'll probably just go to a Liquor Store instead)!
Does this make me happy? Not really (Although the fact that I now have access to ALL THE LIQUOR IN THE WORLD certainly keeps me from becoming too despondent). Now I am left to spend the remainder of my days wondering when the next __________ (<--- Insert Band Name Here) record is coming out.