Bicycle Mechanics - Rusty Cables/Chain

I bought a used bike and it has some rust on the cables and a little on the chain. What is the best way to clean the rust off? Rust seems pretty superficial. I was thinking about sanding it, but I'm not sure if that's the best idea. Also, I'm assuming I should lube them both after I'm done, what should I lube the cables with? Triflow? And do I only need to lube the cables where they make contact with another part? Thanks!

Clean your chain with some mineral spirits on a rag. Wipe it dry. Put the tiniest drop of Triflow that you can manage on each link. Let it set overnight and try to wipe it all off. Don't worry about the rust. If it's just supreficial, this process will make it go away.

Do do your shift cables, shift into your biggest sprocket. Now WITHOUT TURNING THE PEDALS work your shifter as if you were shifting into the smallest sprocket. That'll give you enough slack to free your cable housing from the stops on the frame. Clean them with some mineral spirits on a rag. You can lube them with some triflow if you want, but don't overdo it. I'm not convinced that it's any better than just clean dry cables.

If I need to get an old rusty bike roadworthy really quickly, I spray on some WD-40. It will provide enough lube for a day or 2 and will penetrate into the links.
WD40 is not strictly a lube, it is too lightweight, but is useful for a quick fix.
If the hubs and bottom bracket are OK, keep WD40 away from these as the solvent will dissolve their grease. If they are in dire need of attention and you dont want to strip them down, then you can drizzel some oil into the bearings.

Cables should probably be replaced. Both shifter and brake cables can be under considerable tension, brakes particularly in emergent situations and rusted cables are more likely to break. A broken brake cable can be a disaster. Broken shifter cable an annoyance. Look for stainless replacement cables. If the cables are rusted inside the housings, then probably the inside of the housing is rusted as well. Housings rarely fail however, they just increase shift resistance. A couple of chain cleanings will likely get rid of superficial rust, which is not unusual with chains. Steve

Cables should probably be replaced. Both shifter and brake cables can be under considerable tension, brakes particularly in emergent situations and rusted cables are more likely to break. A broken brake cable can be a disaster. Broken shifter cable an annoyance.
Replace them with Teflon coated cables and teflon lined housing and you'll be running smooth

I use Dremel wire brushes to get rust out of Allen-screw heads, small steel parts, and the like. As long as your chain just has a bit of rust on the sideplates, it shouldn't be a problem.