The best airport to end up at would be Naples itself. Delta Connection fly from Atlanta to Naples a few times a day.
However this is quite expensive so the next best airport is Fort Myers and is only 30 miles up the road. I'm not sure about transportation links but a taxi wouldn't cost too much.
Arriving at Miami then there is a Bus service from Miami Airport (just outside the airport) to Naples. As there is a gap in services between 15:30 and 22:30 you may have a long wait as these times aren't really suitable for European arrivals.
If you are going to use the Greyhound Bus Service from Miami to Naples then you'll probably be getting the 22:30 bus from Miami. You will arrive at Naples around three hours later and the bus drops you off at the bus "terminal" which is around a mile away down Davis Blvd from Wellesley Inn.
The bus costs around $50 return, which is a bargain!
I have used the bus on a few occassions but this year we hired a car... it was so much easier and quicker.
Orlando would need to be a car as it would take an age to get to Naples via bus, if it was possible at all!
One suggestion though... if you are gong to Miami and using the bus then don't get the taxi to the greyhound bus terminal until about an hour before... the taxi will cost about $10. Let me just say that the bus depot isn't the nicest in the world.