Hi Ironsights, glad to have you on the boards!
If the rust isn't deep, your main concern is going to be stopping the spread of any rust and then ensuring that all parts move freely as they should. I would definitely pull every part that comes out and go over everything - you'll want to make sure you don't miss any areas that could grow unchecked to be a problem in the future. The bore on a Chinese SKS is going to be the least likely place to need TLC, they are chromed and often pristine even on guns that are rust buckets on the outside. For the bolt, the firing pin must
be removed and both it and firing pin channel checked and cleaned. If rust has formed in there and you leave it, your chances of a slamfire go up tremendously.
The gas tube/gas piston should come apart and checked as well, the piston should be free to move until ~3/4" is sticking out the rear end of the tube like this (it does not need to be able to travel any farther):
You should also pull the op rod and the spring just under the rear sight block and clean this area out. It also needs to be able to travel about 3/4":
I'd hit the rusted areas first with a simple paper towel dipped in a light oil. If the rust isn't deep, this may be enough to get it up off the surface. If that doesn't cut it, you'll want to try something a bit more aggressive like brass wool, steel wool, or a brass brush. If you go too aggressive, you run the chance of stripping the finish though. It's a fine line, but then again, your SKS isn't exactly a $4000 East German.
Like GM says, make sure to clean after shooting that corrosive Chinese surplus ammo. All your work will be for naught if you just put it away with the corrosive salts still coating the surfaces of this carbine.