American Fox Walkers make decent general purpose dogs. I've seen them work down here in Georgia on deer, and hogs. Some get trained as scent dogs, others as sight/chase and bay dogs. For hogs a lot of guys down here use mastiffs and Pit Bulls as the catch dogs.
Seeing a good team of dogs is really something to behold. Scent dog finds a trail and sounds off, and begins tracking, if they get within sight the sight/chase/bay dogs take off and sound off. The bay dogs will corner and hold game at bay, until a catch dog is brought in to wear the game down or the hunter comesand finishes it off. Some hunters here prefer to catch their hogs live, then let them calm down before they finish them and shoot them. Supposed to reduce adrenaline in the meat.
Don't forget terriers for small game like ground squirrels and cotton tails. You may laugh, but I've got a pretty agressive yorkie that relentlessly tracks down rats along the drainage ditch near our property, and he goes after snakes and lizards too. Tangled with a oposum once and held ituntil my lab got there and finished it off. Unfortunately my lab does not seem to come by hunting very naturally. Heck he retreives well but he never took to letting you have anything back after he got ahold of it. but when that yorkie hits something he will join in. If you find a dog that has the insticts this strong, then work with it. That little dog loves to hunt and get rewarded.
You say "squirrel" and he's jumping at the door.