My chain and my rear derailleur very suddenly went to shit recently, I'm getting weird slack and grinding in the smaller gears and the bike's generally un-rideable. The derailleur's a Suntour Cyclone Mk. II. I was reading up about it and it looks like some owners of this derailleur or similar ones managed to fix its tension by just disassembling and cleaning it, I'm sure this one hasn't been cleaned in a very long time so I figured it's worth a shot.

I'm still kind of noob at bike maintenance and I don't want to fuck this up. What materials/methods do you use to deep clean a rear derailleur? I have a tutorial on taking the thing apart, but I don't know what it's best to clean/lube it with once it's like that.