Claremore is a pleasant town, lots of outdoor and cowboy types. Plenty of good fishing in the area. It's close enough to the urban stuff in Tulsa to make it easy to get anything you want there. Like a lot of smaller cities 30 miles from a larger city, it's becoming a commuter or bedroom community. The landscape is rolling hills, mostly ranching and not as much farming. Climate, people, landscape, and gun laws are not that different than northwest Arkansas. In fact, the Walton family's in-laws, the Robsons, used to be based there and may still be, so there's another Arkansas connection.
There's a good gun store in Claremore, but it's mostly oriented towards hunting guns. Tulsa is a major hub for guns - a gun show just about every ten minutes, lots of good gun stores, and a northside gang war going on right now to remind you to carry your piece!
Lots and lots of gun clubs in the area. Red Castle is on the other side of Tulsa, so it's a little bit of a drive from Claremore. Oil Capitol is east of Broken Arrow and much easier to reach from Claremore, though more expensive. There are a few others mostly focussed on skeet, trap, and sporting clays, but Red Castle and Oil Capitol have about everything - IDPA, IPSC, shotgun sports, rifle ranges, etc.
One thing you definitely should be aware of in Claremore is that a very large percentage of the population has a small amount of Cherokee blood, and is proud of it. Most don't look Indian at all; in fact our Congressman, Brad Carson, is one of those blond-haired Cherokees.