Don't move to Louisville. Plenty of people who live there love it, but I lived there for six months and hated. Still hate driving there when I visit.
I live in Lexington, and have for over a decade. Moving to Frankfort (the capital) soon. There's a VA in Lexington, so that's an option for you. Plenty of rural land in surrounding counties if you don't mind a commute.
I've seen open carry, and done it, in Lexington, but it's rare. No one ever freaked out. Concealed carry is extremely common. We don't have gangs, really. We have people who think they're in gangs. I literally live in one of the poorest, most crime-ridden neighborhoods in Lexington currently, and the guys that think they're "hard" would be a joke in any other city's "ghetto" area.
Folks covered most of the other things to know. Don't move to eastern Kentucky. No VA or jobs there, and lots of pills and meth. A fair amount of meth in western Kentucky as well. Really, central Kentucky is the way to go.
There's public hunting land, but I wouldn't hunt it ever again if I didn't want to take the risk of getting shot by an idiot who shoots his rifle once a year. (I've hunted public land and won't ever again.) With that said, you can find private land to hunt if you do a little networking. Or just buy some acreage outside town and fill your freezer from your front porch.
Yeah, there's elk. It's an introduced herd on reclaimed mountaintop removal strip mines. There's black bear, but the season is like two days long, and only in a couple counties. (To give that some scale, Kentucky has 120 counties.) They aren't counties you'd ever want to drive to.
Rifle season for deer is either one week long or two weeks long, depending on what "zone" you're hunting in. Counties are divided into one of four zones. Zone 4 is one week, antlered only. Zone 2 is one week, any deer. Zones 1 and 2 are two weeks, any deer. You can take up to one buck and three does (with extra tags) in the "any deer" zones.
I hunt with SBRs and suppressors. Only NFA that isn't legal for hunting is machine guns.
You can own all the "evil black rifles" you want in Kentucky. No regulation of firearm features or magazine sizes. I suspect there never will be. Kentucky loves guns.
The social conservatism might get under your skin. As a libertarian, it gets under mine. Alaska was a damn sight better on that score. (Spent two years there.) But there's plenty of freedom when it comes to guns, cars, etc. (No emissions or inspections for cars.)
Hope that info helps.
Aaron