Welcome to the forum Barney,
Brasso is also used a lot here. Goes back to the army days and polishing brass every day.
One thing with Brasso, use a soft cloth and light strokes if you are just doing tarnish. If you have deeper scratching, use terrycloth and more pressure and it will take as much out as you want to work on it. But when doing deeper scratches, I always finish off with lighter strokes with the softer cloth.
Buy Brasso in as small a can as you can find. I bought an 8oz can a couple years ago and still half full or more.