Just click on an airport to go to its website:-
Fort Myers (RSW) The closest airport to the house, just 20 minutes door to door, and in our experience very quick to get through. There is a brand new terminal that has just opened. All the major US airlines all fly into Fort Myers. There is talk of direct flights from the UK, including Virgin Atlantic from London & Manchester, and BMI from East Midlands. But for the moment, there are good connections from US hub airports (Atlanta, Philadelphia, Chicago, etc). If you are a European guest travelling to Florida in the winter and you are taking a flight that connects in the USA, you might want to consider the likelihood of your connecting airport being shut because of bad weather before choosing your flight / route.
Miami International (MIA) If you want to use the closest airport with direct UK flights (from London only at the moment), this may be the one for you. It's just 1½ hours drive to Fort Myers, and recent feedback from guests says it's an easy journey.
The other option for direct flights from the UK is Tampa International (TPA) On the Gulf Coast, also about 1½ hours easy driving from Fort Myers. Nice airport, good facilities. Great drive down over the spectacular Sunshine Skyway Bridge across the mouth of Tampa Bay, with pelicans for company!
Orlando International (MCO) This is the main port of entry into Florida for many UK guests, especially those spending some time at the theme parks. Used by most scheduled carriers, including Virgin Atlantic and British Airways. It's at the southern end of Orlando, closest to Kissimmee and to most of the Disney parks. Has direct scheduled flights from some UK airports. Usually an easy drive down to Fort Myers, about 2½ - 3 hours.
Sanford International (SFB) Used by most of the UK charter airlines that fly to Florida for a Disney-based holiday. At the northern end of the Orlando conurbation, 30-40 minutes from Orlando International.