I would say that for $1000, you get get 2 rifles, one for each critter. For hogs, I do like the semi-auto concept - I've used a .270 BAR, M1A, and my old Win Model 100 in .308Win with great success on Porky's there in Osceola Co. I've also used muzzleloaders, cap & ball revolvers, 20GA shotgun, and a .357Mag pistol on them as well - all work well. It really doesn't take a whole lot to kill those FLA ferral hogs if you make decent shots.
Any of the above or an AK or SKS derivative, or .30-06 of any type, even something like a Beretta CX-4 Storm carbine in .45ACP would be a marvelous choice.
For deer I would go with just about any decent rifle of .243 cal or bigger. I'm a big .308 guy, but that's just me. Savage offers a lot of nice shooting rifles at reasonable prices and that is probably the route I would go if in your shoes.