As far as historic sites, Fort Ticonderoga would probably be the one most worth going to. I know, I know...It's not even in Vermont, but it's close enough, and it was captured in part by Ethan Allen and the Green Mountain Boys. Mount Independence is nearby (in Vermont) and has trails going to the remains of Revolutionary War fortifications.
Gun shows will be scarce and I've never been to one in Vermont so I don't know if they are any good. If you're in the Burlington area and looking for a gun shop, Powderhorn in Williston seems like a popular place. I've only been there once, but they were more than willing to let me handle whatever I wanted to see.
I don't know of any places to shoot that don't require memberships, but I'm sure they are out there. I've heard rumors. Ask around. There is a place to shoot trap and 5 stand in Williston if you're into that (
http://www.shootncsc.com/About.html). I've just gotten into guns within the last year, so I'm not too familiar with all the gun related opportunities around here.
If you're into the outdoors, there are lots of day hikes you can do. Mt. Elmore is an easy hike and there is a fire tower you can climb at the top. Mt. Mansfield is a nice one too. You can take the Gondola part way up and then hike to the summit. Or if you don't want to spend money on the gondola you can hike the whole way. If you find the marker at the summit, you can stand on the highest point in Vermont.
There are decent beaches in Burlington on Lake Champlain.
That's about it. If you like beautiful mountains, relatively few people, and good gun laws you're coming to the right place.