Due to the housing market here, you probably are going to be quite limited as to buying anything, anywhere.
From what I have been told, the issue is no inventory. Whatever hits the market is gone in hours or a day or so and usually comes with multiple offers over asking. Another concern I would have if I were looking in this market, is it sure would be a good time to unload a dog of a house, or one in a bad area, issues/problems with the house, etc. In other words, see it first hand.
Unless you can arrange temp housing such as a rental or apartment, you will have to possibly buy sight unseen. No way I would do that, but that’s me.
Other than the usual disclaimer about some parts of the city, primarily east side, there’s not a lot of truly bad areas. But there are other issues to be aware of, length of commute, close by amenities, etc. that only come from giving it the once over by being here.
As for gun ranges, ORSA is your best bet. It is in Oak Ridge. Depending on where you’re coming from it can be 20 minutes to 45 minutes or so from Knoxville. Google Oak Ridge Sportsman’s Association for more details. It has up to a 1,000 yard rifle range. Some caveats do apply as to use such as competition only.
ETA: Not aware of any quirky gun laws per se, as I don't know your laws in UT. I do know our background check is state run as opposed to the Feds, sometimes it gets pretty backed up as has been the case lately with the gun market.
As an illustration of the current housing market. I have a friend who had a home in a fairly affluent section of town. It was an older home but was in some serious need of updating. Of course you always hear location, location, location and his definitely had that for it. He puts on the market as is, where is. And he puts a hefty price on it. Less than 1 day later he has 5 offers ALL over asking price. The people that bought it were in another state and only viewed it online. My friend made the stipulation that the buyers had to come look at it in person before he would ink the deal as he did not want them backing out at the last minute although he had multiple backup offers. It is that hot here.