If you’re looking to get your hands on a plane to fly in GTA 3, then there’s one waiting for you at the airport. You’ll need to reach the third island and get yourself to the airport. You can’t fly the vast majority of the planes in the airport, although there’s an exception.
Smash through the barrier and go to the far corner of the airport in the south west corner. There waiting for you is a Dodo. They are frustratingly difficult to fly, but re-spawn so you can practice as much as you want. To make things even easier park the Dodo in a garage at one of your warehouses and you can just jump straight in.