The lowest cost option would be
TassieLink I think.
I've used the service at both ends, flying into Launceston and out of Hobart. They will also forward and store any baggage you don't want to take on the track.
You do need to plan your walk around the bus timetable.
I have stayed in the Waldheim Chalets a couple of times - nice, and convenient, but the backpackers bunkhouse at the caravan park is probably the cheaper option, and not far from the tavern for a good feed and a beer.
Last visit (in October) I just got off the bus around midday, took the next shuttle to Lake Dove, signed the book, and walked straight through to Waterfall Valley. It was only snowing (sleeting) a little bit. From Lake Dove (or Ronny Creek) to Marion's Lookout is the hardest but it's not too difficult.