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...Schwinn paint was pretty good stuff, as was their chrome. It's doubtful any paint you put on it will be as durable, so I'm +1 on the advice to take it apart, clean and polish the existing paint, clean up the components and regrease everything that uses grease. I commuted for a couple of years on a Schwinn collegiate ladies frame that was an outstanding color of purple. They're a little heavy, but very well constructed and durable.

From your photos, I can't tell whether you need new tyres, chain, and brake blocks. But it you intend to keep it and ride it for a while, those are the tings you would want to replace with nesw stuff. The Schwinn rims in the 26" size were a special tyre, Schwinn S-5 was the designation.