It really depends on what you like. I personally prefer to hunt deer and rabbits, but that is because I hunt with dogs. I use a 12 gauge shotgun for both (I am a poor college student, so I don't have a 20ga or 16ga) where I hunt in eastern Virginia you can't use centerfire rifles during deer season.
If you have experience with trap or skeet, then you might like birds more.
And then there are Turkeys. I have a bunch of friends that LOVE to hunt them. It takes a lot of skill to do successfully (on you own).
The best all around gun (as mentioned above) is a shotgun, and I would say a 12ga. I have been shooting a 870 Wingmaster since I was 12 and have never had a problem getting it around or tiring me out (but then again at 12 years old I was 5'11"). Now my deer gun is a Mossberg 535 with a 22" barrel, and the 870 gets the lighter field work, and will be all but completely retired when I find a Browning Light 12
that I can afford.
However, to get started, take the hunting course offered by Florida's Department of Game and Inland Fisheries. They will tell you everything you need to know about hunting (mainly in Florida, but most of that information transfers to neighboring states).
Good Luck and enjoy.