I started the cleaning on the parts with a wire brush attached to a power drill. This cleaned off most of the rust, dirt and old paint. This would propably have been fine if didn't care how the tool looks. The steel was far from shiny.
I started sanding with 200 grit sand paper to clean the surface a little more from the small gaps and other areas the wire brush did not clean up so well. When sanding/polishing you usually want to double the grit number of the paper you are using. I sanded pretty much everything exept the threads of the screw. I wanted to clean every little detail I didn't want dirt and rust for example in the hole around the wheel just because I was lazy.
Therefore next I started the polishing process with a 400 grit sandpaper . When polishing surfaces you usually want to sand only in one direction with every roughness of paper you are using. This causes lines on the surfece you are sanding. Then when you switch to higher grit you change the angle of the direction you are sanding in which allows you to see when all the lines caused by the lower grit paper has disappeared. Then you know that you can move to higher grit. In this case I did not use that method because the shape of the tool did not allow me to change the direction (of sanding) a lot. In addition the surface was not so smooth that a few small scathes in the finished surface would make any difference.
After 400 grits, I moved to 800 grits. Then I moved to 1500 and ended with 2000 because these were the paper I happened to have already. It's important to remember that as you sand the paper will get stuff stuck to it and the paper will become smoother. In reality when I finished with the 2000 grit paper the result was already a lot smoother what it would have been if I had changed the paper more often. I guess the finish at this point it was somewhere between 2000 and 3000 grits.
While sanding it's also important to remember that you are constantly removing material from the surface. If you remove a lot of matrial the parts will be moore loose. For exmaple, I did not sand the hidden part screw any more than I had to in order to clean it up, because I did not want the parts to have too much room to wiggle after I attached them back togerther.