Rumour has it that Aviapartner is substantially cheaper than the KLM Jet Center for SEP aircraft handling. They're active at Rotterdam and Schiphol as well. Worth a call.
From the Schiphol main terminal it is indeed a 15 to 19 minute train ride into the center of Amsterdam (watch out for pickpockets on this line). But the GA terminal is at the other side of the field so you have to find a way to get around. I don't know if the handling agent will bring you, or whether you need to take any of the buses that circle the airport. Or you can get a taxi straight from there into the city center.
The direct train from Lelystad to Amsterdam Central Station takes 40 minutes and you've got the same issue of getting from the terminal to the train station.
The full public transport planner at
9292ov.nl: OV-reisinformatie en routeplanner voor bus, trein, metro, tram en veerboot will give you the details. Best I could come up with is 1:11 for Lelystad to Amsterdam and 0:32 for Schiphol East to Amsterdam. From Rotterdam it's 1:31 and from Hilversum 1:19.