I'm located in Massachusetts (near Cape Cod) and sunrooms on sonotubes are common in this area. The reason is cost. Your 14' x 20' sunroom would typically have three sonotubes (10' on centers) with bell footings sized for the bearing capacity of your soil, and the weight they must support. Floor joists are typically attached to the existing dwelling with use of a ledger board. They are typically constructed as a hybrid post and beam structure with walls framed in as needed based upon size and location of windows.
With that said I prefer like stated above to have at minimum a cast-in-place concrete foundation to support the sunroom. This can be a full depth basement or frost wall (minimum frost depth, 48" in Mass). The reason is most people after using their sunroom during the warmer months miss its use during the winter and want to go to a year round occupation. A foundation under it makes this a lot easier and less costly.
Even though these are three season rooms not intended for use during the cold New England winters we do have minimum insulation requirements in Mass. You may want to check with your building department and find out what requirements you will need to comply with. This link will provide you with information on codes in Vermont
http://www.reedconstructiondata.com/building-codes/vermont/
Verify the code information with your local building department.
Good luck!