We have done this route several times.
We do I-10 all the way to I-49N to I-30W. At state route 69 go north to route 82 then west to Gainsville. 69 is a good road, but 2 lane.
The roads thru MS are terrible, windy, hilly, many towns, many rough but least distance.
2015 Fleetwood Discovery 40E on a Freightliner XCS chassis with a Cummins ISL9 pulling 1 and/or 2 motorcycles, '07 Honda Accord OR a 17' Runabout Boat.