First be aware that in February, the Panhandle can still be chilly , especially at night. Are you looking for full services or willing to dry camp?
I loved Appalachicola National Forest but most if not all camping areas are primitive and you are pretty far from the nearest grocery or gas station. By Primitive , i mean o electric or water at sites
Lake Seminole on the Florida/GA border is really nice. Corp of engineer campgrounds and 1/2 price for seniors.
Pine log state forest, near intersection of routes 20 & 79 offers sights with water and electric and its in close proximity to Panama city beach. A little rustic but the price is right.
I'm not a beach guy (prefer shade) so I'll let others comment on those