Just from my experience:
All of the folks recommending the larger wire are on the money if you're going to use the circuit for anything near its capacity.
The autotransformers (variously known as Variacs or Powerstats -- which are trademarked names) do indeed cost that much new from a supplier. You can find used stuff on fleabay or at just about any ham radio flea market. You can find a 20A unit for under 50 bucks if you look around. If going that route, make sure that you get one that's rated for single phase, 120V, 60 Hz. Avoid ones made for three-phase, 277/413V or 50Hz.
If you're only every going to use this for lighting and the occasional use of a shop vac, I wouldn't worry much about voltage drop.
When I wired my shop, I ran 6/3 out there with a 60A breaker at the main panel in the house. The electrician and the building inspector both wanted to see that UF wire 2 feet down. This is really a good idea anyway, since it virtually eliminates any chance of anyone ever accidentally hitting the wiring. Part of my run was only 12" down and we put that in galvanized conduit. I don't have to worry about hitting wires when planting hostas. :jiggy: