There is now a connector from the airport to the Montour Trail. It starts pretty much right off of the pedestrian walkway that leads into the parking lot. You would be welcome to stay here. Friday night arrivals are always best. But I can make do any day.
Your options for getting to the GAP would be to take the Montour Trail south (about 63 miles) or go through the city (about 35 miles).
If you take Amtrak then you should arrive early morning and take the Pittsburgh route.