Some people harvest good game with less than 5 acres, if the land is situated such that it is a major game highway between feeding and bedding areas (deer I'm talking), esp. if it's a bottleneck. A small amount can also suffice if you bait them with a feeder or food plot, salt lick, etc.. It's gonna depend heavily on what all species you want to hunt (for ducks you'll want ponds, etc.), whether you're going to bait, what the natural terrain is like, and what the neighboring lands are like (pristine wilderness? does anyone hunt the neighboring lands? etc.). You also want to be able to control access to your land to allow deer in but yahoos (humans) off. Meaning barbed wire fence which deer can jump, posted with no trespassing signs. I'd buy around 20 acres in a pristine area, preferably adjacent to a non-huntable area (wildlife refuge or national park), OR adjacent to huntable public lands, from which the deer will clear out on opening day; and preferably with a good amount of water (1 or 2 ponds; and/or a stream); then spend the rest of the money on:
-good fencing & signs to keep others out,
-your hunting shack with a heater, strong doors & locks, etc.
-building a road on the property to access where you want to build your shack (though if you build it just on the edge as you're coming onto the land, you won't need to build a road, which is actually preferable so as to leave the main of the land intact and unaffected by your activity. However, if you build a food plot or have feeders, you'll need to at least clear a 4-wheeler trail to cultivate & maintain your food plot or feeders). In some of those lands in the hills of KY & TN, there are very few crops (too hilly and/or rocky), so there are no "natural" feeding areas for the game; hence it makes more sense to make a food plot than it would in crop-abundant Indiana, for example.
I think the key, as always with real estate, is location, location, location. I'd much rather spend $1,500 an acre for 20 acres in a good spot adjacent to a wildlife refuge for example, than spend $800 an acre for 38 acres in a place where lots of people hunt and/or live on the adjacent lands and thus decrease your "quiet enjoyment" at a minimum, and at worst, roam onto your land uninvited, poach your game year round (even if only on THEIR land, etc.). Location, location, location! Water is very important too. You can't anchor game very well if there is zero water on the land. Obviously, you want a pretty good amount of cover for game as well - preferably at least 50% wooded; ideally more.