I've taken this too many times, to Miami though.
I-10, and when you get to Baton Rouge, change to I-12. I-12 will merge again with I-10 again later. This route saves you time since I-10 loops down to New Orleans in this area and then back up. If you want to see New Orleans, stay on I-10 but the trip is long enough without the "loop."
Then when you get to Florida, take I-75 south as if you were going to Gainesville or Ocala. Be sure to stop at one of the Florida Citrus Centers, it's a nice tourist spot that's all about oranges and citruses!
Then on I-75, by Ocala, take the Florida Turnpike. It's a toll road, but the trip is generally smooth and the service stops are generally comfortable. To save money on the toll road though, get off of it when you are near Fort Pierce and take I-95 south to West Palm Beach. You shouldn't spend more than $12 in tolls taking this route.
Taking the turnpike is less stressful and actually quicker than taking I-95 down from I-10. I-95 is a mess and full of construction. Plus that's where the majority of people live - by the coast, and you won't get to see much of the coast from any freeway.
Also, there are nice rest stops in Louisiana (some of them) and Alabama. So take advantage of that and be prepared!
The link I provided below is the toll calculator for the turnpike.