Your question is too broad. Vintage classic under $250 - could be anything from a 1974 Peugeot UO-8 to a 1992 Bridgestone MB-2 to a 1988 Cannondale SR400. Vastly different bikes, all perfectly suitable for commuting in the right circumstances, all usually $200 or less on Craigslist.

But your instinct is, I think, sound. Older bicycles offer tremendous quality and interest for the buck.

It is almost mandatory to have the ability, and the few inexpensive tools needed, to perform basic maintenance and overhaul. If you have to pay a bike shop $100 to overhaul every used bike you buy, then it will be harder to get a very good bike for under $250 all in.

Go lurk on C&V for awhile, figure out generally what you want. Learn to tell what size bike you need. Then ask in the Appraisals forum. Link a couple of Craigslist ads and ask if this looks like a good bike at a good price for the intended use that you describe.