Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Panama City Beach to Savannah as you normally would.
For a flight from Panama City Beach to Savannah, you will be flying into Savannah/Hilton Head. Savannah/Hilton Head (SAV) is just 7.4 mi from the center of the city. Savannah/Hilton Head is the only Savannah airport and it handles 0 inbound flights from Panama City Beach per day. 3 airlines have flights to Savannah/Hilton Head from Panama City Beach on a regular basis.
The most popular airlines flying from Panama City Beach to Savannah are Silver Airways, American Airlines and Delta. Something to consider prior to booking your flight.