The Everglades is an unbelievable place. The spring can be a great time to visit. There should be snook, redfish and tarpon making their way along Gulf edges and laid up in secluded lakes and coves in the back country. If you can it would definitely benefit you to hire a good guide. The area is so vast that a novice will find themselves struggling to find fish.
As for Charleston, I am not sure what the fishing will be like. A lot of the redfishing that I have heard about in that area is done on the summer new and full moons where the redfish will push way up into the spartina grass searching for crabs. I think that Byron and Paula have had success fishing around Hilton Head in the spring.
Good luck, let us know how it goes.