I-10 is good road along that route. We just drove it two weeks ago from Jacksonville to Houston. Most of the rough portion is west of Baton Rouge. It is pretty much flat and the bridges are easy to travel.
There are a number of RV parks along that route. We overnighted at Eagles Landing in Holt, FL. It is not a fancy park but convenient off I10, $25 per night for a level, full hook up site. I would call ahead to reserve a site since they seemed to fill up by end of day when we were there couple of weeks ago.
2007 Country Coach Allure Siskiyou Summit, sold/traded Nov. 2018.
2019 Grand Designs 384GK-R 5th wheel. Glen Allen, VA