hi,maybe can help a bit here.i'm a proffesional watch polisher.a simple advise here.to polish a watch proffesionally,you will need a lot of proffesional tools.i will take photo of some common tools used and different polishing compound next time.
using autosol only can make your watch looks shinner but in other way also ruin your watch shape or angle if you polish in a wrong direction or wrong way.in watch polishing ,there are three different finishing
first * mirror shine
second * hairline brush
third * sand blast
to do some home polishing,you will need at least three different grid of sand paper,lets says 400,1000 and 1500.use the smaller grid to remove the deep scratches follor by the bigger grid.finnally by 1500 or 2000 untill all the deep scratches removed after all this,polish it with autosol with some cotton cloth.this parts is for mirror shine finish.
for hairline finish,home diy can use different sand paper grid to archieve the hairline result.
sand blast can only be done by sand blast machine inside chamber
all the polishing tips above just as tips,if you damage your own watch,dont blame me.againt,good job need years of experience..
will piost the photo when i am free