Your 30-06 will work for coyotes. If you plan on keeping the hides, you may have to do a little stitching. A shotgun will also work.

After you get into it a little more, you may decide you want a dedicated predator rifle. Any of the .22 centerfires make great predator rifles.

Most of my rifles are bolt actions, but semi-autos and single shots work fine, too. Usually bolt guns and single shots are plenty accurate, but some of the less expensive semi-autos are not. If someone goes the semi-auto route, an AR is probably the way to go.

I just recently picked up a Franchi I-12 shotgun, and I have been taking it out, especially at night, when I've been hunting. So far, I've got nothing but good things to say about it. A lot of this area is pretty brushy and shots are close, so a shotgun is not at much of a disadvantage.

I'm not much of a squirrel hunter, but my great grandfather was a die-hard squirrel hunter. He went out and shot 3 squirrels every Sunday for dinner with his Ithica 20 guage. His was a pump, but if it were myself buying a shotgun, there is no way I would not get a 12 guage semi-automatic. There are a lot to choose from, and many shoot 2-3/4" and 3" shells, which will work on squirrels, predators, and nearly anything else you care to hunt with a shotgun.