First off, be clear about it: there is no cheap way to go to the Antarctic. We chose the Hurtigruten Fram because we had cruised with them before and had great confidence in their competence. There are more luxurious and expensive ships but none that are more seaworthy. A very good value.
The cruise officially began in Buenos Aires. We spent a week there on our own so had not purchased an airport transfer from Hurtigruten for the charter flight to Ushuaia. This became the source of some stress when we belatedly learned that our flight was to depart at 4:40 AM, meaning finding a cab on our own at 2:00 AM. If we had known about the ridiculously early flight in advance, we would have spent the last night in Buenos Aires with the Fram group.
We were met at the airport in Ushuaia by Fram personnel. No problem with check-in on the ship, and our luggage was already in our cabin when we arrived.