Charlottesville–Albemarle Airport: The sensible option is a rental car or rideshare/taxi; there is no airport public transit. Pantops is roughly a 20–25-minute drive, depending on which side of the US-250 commercial corridor you are staying on; expect roughly US$25–40 by rideshare before surge pricing. Rent a car here if Monticello, wineries, or the Blue Ridge are central to the trip.
Charlottesville Union Station (Amtrak): Amtrak's Northeast Regional, Crescent, and the three-times-weekly Cardinal stop here. The station is between UVA and the Downtown Mall, not in Pantops: take a rideshare/taxi for the practical 10–20-minute, roughly US$12–25 trip east to Pantops. CAT and the free trolley are useful around Charlottesville, but are not a luggage-friendly Pantops transfer.
Washington Dulles International Airport: Use IAD only when airfare or an international connection makes it worthwhile. The least painful car-free route is the daily Virginia Breeze bus to Charlottesville, then a rideshare to Pantops; allow a full 3½–5 hours door to door, plus the connection, and check that day's schedule. Driving/renting is about 2–2½ hours in normal conditions; an Uber all the way is poor value.