Your problem will be Mardi Gras which falls on Tues March 5th this year. One Louisiana state park that we like is Palmetto Island State park south of Abbeville in cajun country, we were there in our coach last weekend, but unless you luck into a last minute cancellation you can forget getting in there the weekend before Mardi Gras. I checked their reservation site back at Thanksgiving and they were already booked for Mardi Gras weekend at that time. Surprisingly though when I checked at Thanksgiving they had vacancies every day until the weekend before Mardi Gras.
As to the question of good routes, there are none, I-10 is probably the best, the other east-west highways all have issues, TX105 is not too bad until you get within 10-15 miles of Beaumont, then the pavement gets rough. All the Louisiana highways south of I-10 have issues, you just get to pick if you want all your awful teeth jarring pavement in one stretch or broken up over multiple shorter stretches. It is possible there is some zig-zag route of smooth or at least not bone jarring pavement across south Louisiana, but if there is I have not found it yet.
If you want the scenic route, I would take the coastal route option, I-45 down to Galveston, cross the ferry to the Bolivar peninsula, hwy 87, to hwy 124, up to Winnie and then hwy 73 to hwy 82 in Port Arthur, then across into Louisiana, cross the Calcasieu river on the much smaller ferry at Cameron, and follow hwy 82 to Abbeville, (stopping off at Palmetto island state park if you can get in), spend some time in the Abbeville area, see real cajun country, tour Avery Island, the Tabasco factory, visit Jungle Gardens, go over to Jefferson island, tour Rip Van Winkle gardens, eat some cajun food at any number of authentic mom and pop restaurants (the cafe at Rip Van Winkle gardens has some great slightly more upscale cajun food as well), then continue your route to New Orleans on Hwy 14 then down Hwy 90. Just be aware parts of Hwy 82 in Louisiana are going to be rough.
