Schwinns enjoy a nostalgia premium, and tend to sell for quite a bit more than better vintage bikes that do not share that premium.
While a Varsity may well bring $200, its one of the heaviest road bikes ever made, has bottom end parts, steel rims, etc.
For the same budget, you should be able to find a bike that is 12 pounds lighter or better, alloy rims, three piece alloy crankset, better components, etc. Learn what makes one bike so much better than another, then pounce when you see a deal.
We talk about affordable bikes that make good commuters all the time, at least once a week. Do a google search of the forum, and you will find endless recommendations, well within your budget.