I’ll be driving this in early November - new part of the country for me and I have no idea what is best.
I welcome any and all suggestions for routes and things to see along the way.
Lots of options on routes.
Pepsicola-Mobile-Birmingham-Mempho
Pepsicola-Mobile-Hattiesburg-Merridian-Tupelo-Mempho
Pepsicola-Gulfport/Biloxi-Hattiesburg-Jackson-Mempho
Depending on the route you take and whether you want to spend the night along the way, you may want to look at the football schedules for University of Alabama, University of Southern Mississippi, and Mississippi State, as that will affect traffic and hotel availability.
Things to see along the way–
Mobile has the battleship U.S.S. Alabama and submarine U.S.S. Drum you can tour.
Biloxi/Gulfport has Beauvoir (home of Jefferson Davis) as well as casino gambling.
I think Birmingham has a museum about the Negro League baseball team.
Jackson has the Medgar Evans house/museum I think (slain civil rights leader), a zoo, an agriculture museum/exhibit area, an art museum, and a planetarium
Tupelo has the Elvis Birthplace, a car museum, and a buffalo park (outdoor exotic animal place, buffalo, giraffes, etc).
Memphis has a zoo, Beale Street (touristy area with restaurants/bars/music), Graceland (Elvis home), Mud Island (museum/exhibit about the Mississippi River), and is about an hour from casino gambling in Tunica, MS. There’s a blues museum, and a restaurant owned by Morgan Freeman in Clarksdale, MS–not too far from the casinos, and if you’ve got a soul you don’t mind mortgaging, you can go to the intersection of U.S. 61 and U.S. 49 and get some guitar lessons at midnight…
And …
Birmingham Civil Rights Institute. When I was there they had the actual cell door from the Birmingham jail when Dr. MLK was detained.
Vulcan, the world’s largest cast iron statue. What a view.
Sloss Furnaces National Historic Landmark. It really is haunted.
Dreamland BBQ. Based out of Tuscaloosa.
If I were going to take this drive I believe I’d go Mobile-B’ham-Memphis. Although you could come through Jackson and have lunch with me instead if you’d like, much of Mississippi that you would pass through on Biloxi-Jackson-Memphis route is on the flat side and very rural. I myself get sleepy driving up I-55 North. 
Since the OP is seeking advice, this is better suited to IMHO than GQ.
Colibri
General Questions Moderator