Don't worry about the rust. Just keep the chain clean of dirt.
Prepare a soda bottle, degreaser, cassette brush and lube
Fill the bottle with some degreaser. Take the chain off, put it in the bottle with degreaser and shake it vigorously. This should clean the chain fairly well of built up dirt. fish out the chain with a tool or coat hanger and clean off with water. make sure chain is dry before applying lube.
Clean the cassette and chainwheel with the brush. You only need to get the dirt off.
Put the chain back on, and you're done.