Personally, I would move to a colder climate. Because zombies are undead and hobble, it means that they are through a certain point of rigor mortis...the cold climate would freeze them, thus hindering their movement, or stopping it entirely.
I would not use any sort of gun - the echo of the shot would attract more zombies, bringing hordes of them to your location. Zombies do not base their attacks on sight, but more or less sound and smell. Why else are they so good at finding you at night, especially when crows have pulled their eyes out of their sockets? For my weapon, I would use a spade-head shovel. Why? Reasons:
- It is long - it puts distance between me and a zombie
- It is sharp - the spade end will sever a head if sharpened correctly
- It is versatile - you can use it to put out camp fires, bar doors, hop fences, bury feces, bury your dead, defend yourself against other humans that survived the apocalypse, etc.
As for staying in one place - bad idea. Like I said, sounds and smells attract zombies. Staying in one place too long will make them swarm your house. Eventually, they'll get in or you'll starve to death. The best choice is to move around as much as possible and seek higher ground, like on top of a building. Zombies, "historically", cannot climb...that's why I was a little miffed by Zombieland, but the movie was still unbelievably AWESOME!
As for being in a group, I would only travel with people who are well-educated about surviving disasters and people who are of use to me. Strong, intelligent, cunning, able to improvise, etc. I would take my fiance for sure, though, because we've already talked about a zombie apocalypse.
Unfortunately for pets...they're a no-no unless they can be useful. I would take my ferrets, but I would only be able to take one - one that can actually ferret (go into holes and grab a rabbit). Other than that, I would have to put all of my animals down before they became zombie snacks (as cruel as it sounds..but I would rather them not suffer and starve because I can't provide for them during that time of crisis).
As for clothes - snug clothing (but comfortable enough to move in) and short hair. The less for the zombies to grab onto, the safer you are.