A "long action" will typically be necessary to chamber any cartridge similar in length or longer than the .30-06. A "short action" generally chambers cartridges similar in length to the .308.
The advantage of the long action is probably obvious - you've access to more powerful cartridges. The disadvantage is extra weight, though not a lot unless you're hunting something like bighorn sheep where every ounce counts.
One can rarely go wrong in North America with a .30-06. However, if Florida deer (not Montana elk) are all you see yourself hunting frequently, you might consider short-action calibers like the .308, 7mm-08, or .243. However, it should be noted also that in addition to deer, the .308 and 7mm-08 are respectable elk/moose calibers in their own right. Again, considering Florida as your home range, I would avoid most, if not all, "magnum" calibers.