Realistically what would you do?
Well, the first problem one will encounter in the beginnings of the zombie apocalypse is other people.
Many seem to operate under the assumption that zombies will start popping up everywhere like daisies. I don't think this is a very accurate or realistic expectation. It will, more likely, spread like any other pandemic. Waves of it will begin spreading through populations (and repeatedly cycling back through them).
In the beginning, more people will be killed from panic-inspired violence, failure of public utilities (because people don't go to work in fear of the disease - zombie or not), and misguided attempts at self-isolation (sealing up all house ventilation to suffocate on the inside, for example). Many will die without ever seeing a zombie.
That's challenge number one - surviving human stupidity.
Challenge number two involves the environment. Food, shelter, and water are all necessities that will be required (food and water more-so than the shelter). Only the most well funded of survivalist mentalities will have estates that can support their existence almost indefinitely - and even then, such things have likely been targeted by human stupidity (don't expect to find any usable crops for the first two years after the collapse of society - stupid people will likely destroy the things in search of food).
Exposure to environmental extremes will kill most of the human population. Lack of sanitary water will do most in. Starvation will follow, with infections normally manageable under current hygiene standards becoming uncontrollable. Our Antibiotic-worshiping society will be culled rather quickly when our muted immune systems encounter the realities of bacterial symbiosis.
Then there's the zombies.
Exactly what kind of zombies we are dealing with will determine exactly how threatening they are (as well as relative transmission methods and effectiveness). If we presume it is relatively similar to rabies in terms of hyper-aggression and transmitted through saliva and cutaneous secretions, the zombies will largely be a nuisance and likely become less and less of a danger as the human population assumes a more 'natural' and sparse population structuring.
If it's something closer to a bio-weapon (Resident Evil/ I am Legend type stuff), it's likely to burn itself out rather quickly. People who fled from heavily populated areas without serving as carriers will survive and regroup to form a metastable society succeeding our own.
I will, obviously, keep my strategy very adaptable and able to respond to the threat I find the zombies present.
More than likely, I'm going to be trying to keep panicking people from tearing up and stealing my stuff.