I disagree with having the setting where guns are uncommon or illegal. The whole struggle with zombie apocalypses are the need to find supplies. If we make the setting too early in the outbreak there will be way to much ammunition to go around. If we set it back a little later, then there will be less. Not to mention most of it will be scattered, it wouldn't be in places most people would expect like police stations or gun stores. It would either be hoarded by a group or hidden/scattered. 

Another way to solve the gun thing is to have the infected attracted to sound, like most are. People would be less likely to use guns if they knew the sound would draw more infected to them. It would make sense for most people surviving later on in the timeline to have at least one fire arm and a small supply of ammunition with them for emergencies. Also most people would likely opt out of carrying large, high-powered artillery, simply because it more cumbersome to carry around and less practical. Also if we add in the threat of other people, larger weapons would be more noticeable and thus less people would carry them around to avoid being targeted.