How to clean security screen door?

While they give us a great feeling of safety, what with the dead bolt and the lock on the knob too, they're getting old and rusty. What's the best way to clean that rust off? Is there something we can just put on a rag and rub? Or should we repaint them? If we have to repaint, do we need to remove the doors and take them in the garage, spray paint or brush, Rustoleum or something else?
As you might guess, we're decidedly unhandy about house things for the most part, but we're going to put the house on the market at the end of the summer and so we're spending the next couple of months getting everything spiffed up.
Thanks for any help.
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