Check rvparkreviews.com and rvparky.com for Bartow, Winter Haven, Lake Wales, Avon Park, Sebring, Frostproof, Polk City, Lake Placid. These are all south of I-4 and will probably be affordable. Sorry I can't directly help you as I live in WH/Lake Wales, so don't frequent the RV parks.
I'm from Lakeland, which is next door to where I live now, and the only one I'd look at there is Sanlan. We've driven through a few times, and it didn't float my boat, but it's worth a look-see.
We do go to Westgate River Ranch outside of Lake Wales. We love it there. There are things to do there-has a cowboy/western motif with a rodeo, but shopping and other activities are 30 minutes away.
There is a park off I-4 in Polk City-LeLynn RV Park that looks like some place I would consider.
Good luck and welcome to Florida!!