You MUST have Operation Arrowhead and you have to play it but I know people that say you can get the original ArmA 2 free version with Arrowhead and play DayZ. Not sure if there's any issue with that. Alternatively you can buy combined ops for $30 vs the $20 of just Operation Arrowhead.
They could be less but I paid $30 for the whole package.
And no single player version. It would be interesting but rather uninteresting since the zombies are very alert and you'd be spending hours sneaking past them alone. Try playing with friends.
My friends and I got a team of 6 and that just encourages you to go ahead and shoot what you want. Zombies no longer become an issue.