The odds of a zombie attack on a huge scale are slim at best, because the areas would likely be quarantined quickly. However, for those within the quarantine, survival would depend on just how hard the government is going to bomb that area. That's something many seem to ignore; a zombie attack would require immense complacency on the part of everyone to spread and fester.
I'm not old enough to use a gun, but I would pack my backpack with a wrench (good reach for cracking skulls), a box cutter (since we have no sheathed knives in the house), cash (to buy things if people still feel that it's valid), my papers (in case of blockades), a bottle of water (to quench my thirst), lunch (to sate my hunger), my cell phone, and change of clothes.
I would head up to the police station with my family, holding my hands above my head while shouting, "WE ARE NOT ZOMBIES, DON'T SHOOT", and hide out there. I won't pretend to have any more experience with firearms than airsofting would give me, and try to find out where we can go next.
Remember, you go to war with the army you have, not the one you wish you had. A knife that you've used your whole life will be of much better use than that brand-spanking-new AR-15.
-Penguin