Both Remington and Mossberg produce some decent three barrel shotgun packages, namely a standard barrel with choke tubes, a shorter turkey barrel with an extra full choke (can be switched around to a lighter choke for upland game in thich brush, home defence, etc) and a rifled slug barrel, usually with cantilever mount so that the gun will keep its zero even when you switch back and forth between barrels. I've got a Mossberg 535 version with 3.5" chambers and a camo pattern that's great for turkey and duck hunting. Such a combination package would probably satisfy 80% of your hunting needs, minus long range varmints and big game past 100 yards.
If such combos are too expensive or unavailable, just the basic shotgun with choke tubes would suffice for everything I've listed minus slug hunting for deer/hogs, etc.
I cannot comment about Kentucky, but my suspicion is that while turkey hunting can be fun (I've been out several times myself), that the ratio of birds harvested for time spent in the bush is not very high. As long as you appreciate that, I'm sure that you'll learn lots of things, such as how to keep comfortable in the woods, familiarize yourself with areas that you'll return to later for other fish and game, and maybe form some other hunting friendships that will help you find better areas, select the right gear and help with learning to clean larger animals that might otherwise be intimidating at first. It takes time for things to come together in hunting, but it pays off in the end. For instance, last season we discovered a wonderful hunting spot for waterfowl in the woods and moved a beaten up canoe to the lake in question. Though we only got two birds that day and didn't make it back later in the season, next year we'll have an excellent spot that we can get to and set up before sun up.
Best of luck with your new hobby.