We've gone from Jax to Tampa a few times.
I95 to St Augustine, onto I75 is a good route, and since you are on a highway, there are places you can stop to get gas, use the restroom, etc, and can feel comfortable doing so.
I10 to I75 thru Macclenny is a good drive, but I prefer the 95 route. This way takes you through Alachua and Gainesville, and I hate driving in Gainesville.
301 is a nice drive, but it does go through Starke, Waldo and Hawthorne---all tiny towns known for speed traps. Speed limits go from 65 to 35 very very quickly, and if you are not quick enough to slow down---BAM, they get you. There was a sign outside Waldo for the longest time, warning people about the speed traps. (Waldo disbanded their police department last year; I think the state patrol does it now.)