Cheap baselayer: silk undershirt from sierratradingpost.com. I think it was less than $20. It's warm, thin, and machine washable.
Even cheaper baselayer: moth-eaten cashmere or merino sweater. Don't throw it out. Throw it in the washing machine to make it snug. Cut off the sleeves if you like. (If you don't have one, check out Goodwill, etc. Make sure it's actual wool, not polyester).