There are a set of winter tires on there already, but I'm not worried about getting paint or rust remover on the tires -- I've ordered some new tires already (going studded this year) and will be getting rid of the ones I have.
How vigilant should I be with rust? Is it enough to wipe it down and clean it up with chemicals or do I need to get out the Dremel tool and sand my way down to clean metal before painting? How many coats of paint should I use?
I think it depends on how bad the rust patches are. If it's just surface rust, I'd clean up the rust with a wire brush and some sand paper and treat the remaining rust with chemical rust remover or converter, then repaint the wheel.
If there is significantly deep rust on the rim that goes deep enough to warrant grinding out, I'd be a bit careful or would just get a replacement rim as I wouldn't want to run the risk that the rim has been weakened. That said, I don't think I've seen that sort of rust on a steel rim that wasn't a several decades old and used in a very damp/salty environment, and even then it's pretty rare.
With rust you really need to grind down to bare metal, then use rust-resist paint as your first layer, covered with a couple more layers of paint to protect that undercoat (depending on how hard-wearing the paint is) otherwise it will just spread.
