Brandon,
What are you using to do your polishing with, bench grinder/polisher, Dremel, die grinder? What kind of polishing wheels are you using?
When using the polishing compound (brown) you want to start by polishing horizontally across the surface of the piece. With each pass you will create a line of compound on your piece. Keep moving this line in the same direction, pushing it up the piece with each pass.
Next do the same process across the piece on a 45 degree angle. This will help remove the scratches and also increase the shine. The more you polish, the better the shine.
Now repeat the above process using the white compound. It will take some time, but you will be happy with the results.
ALWAYS use eye protection when polishing. Also, be careful with the angle at which you apply the piece to the polishing wheel. A bench polisher WILL throw your rings across the room if you are not careful
If you are polishing by hand or need to touch up the shine later I recommend California Custom Purple metal Polish. It's the best hand applied polish I've found. It's applied just like car wax and wipes right off without leaving a black residue. I've used it for years on fuel tanks and rims on semi's. No, I'm not advertising, the stuff just works great.
If you have anymore questions, just ask. I hope this helps.