We've used WalMart a few times for overnights when trying to get from A to B and tired. Not a campground, but can be a good rest stop, with caveats regarding noise, lights
Since this is your first trip in your new camper, I'd think about miles, times, and a learning curve before exploring the world of Walmart parking lots.
Your trip from Memphis to FL will be long. Then, you want to check out the camper, learn all you can, and put it to use. This cannot be accomplished in a Walmart, or Flying J, or a rest stop, even if you find a safe, clean and quiet one, in my opinion.
Take a little time to learn, enjoy, and savor your new purchase. Book a campsite in a real park or cg near the previous owners for your first night. If you have questions, or problems, that night or the next day, they'll be close by with some info, and you'll already be in a cg with people who know (at least a little) more than you do about rvs and camping in general.
This is not meant to be a discouraging post. (I just read it.) Just to be realistic. It's more tiring to drive with a trailer in tow, and you need to allow a little time just because it's a new experience.
I hope you enjoy your new world of fiberglass rving, and hope to see you somewhere on the road.