Can't think of a specific thread, since it comes up frequently....
Airlines are inconsistent in their practices. Officially they will charge you for a full-sized bike, in practice they do not always charge. But it's painful when they do -- $100 and up per trip.
They should not charge for a folding bike in a (more or less) normal-sized suitcase. However, they will definitely weigh your suitcase and charge you if it's overweight (usually 50 lbs).
Samsonite F'Lite works fine for my Swift. Wheels are helpful, the handle is pretty strong.
Make sure you pack your bike in a secure fashion, and include instructions on how to repack. The TSA may decide to search your entire suitcase.