$100 is a great deal for that bike...if you know how to work on bikes.
The second I see "rusted chain" I think it's been poorly maintained (kept outside too) and probably needs an overhaul, not just a tune-up. Don't be surprised if it needs $50+ in parts right off the bat. New chain, obviously, maybe new cassette, cables. The tires may be in fine shape and just need new tubes. Could probably stand to be stripped down, cleaned up, greased, and re-assembled. That might take a pretty penny if you let the local bike shop do it and you might end up finding one in better shape used for that money. Hard to say without seeing the bike in question.