I was in a similar situation to yours about two summers ago. I found a Free Spirit (department store bike "similar to Schwinn") that had been abandoned in the basement of the apartment I was living in. I considered investing considerable amounts of time and money into it to make it fixed-gear but eventually I just put a coaster-brake rear wheel on that I got for free at a local bike co-op after a few weeks of looking around. My bike has a very similar style to yours (same handlebars and seat) and looks and rides alot better with the coaster-brake setup. I added fenders to mine and it's now my rain/crappy weather "beater" bike. I believe if you were to just look around for a coaster-brake rear wheel, which can be found relatively cheaply...try craigslist.com or check out any local bike co-ops, you would be very pleased with the end result and not have invested too much time or money. I ended up using the money I saved to buy a new fixed-gear and now I have two bikes and couldn't be happier.