Some use Brasso, but IMO it's messy. I used Brasso for years but after I joined the Navy they use a product called Nevr-dull. There are hundreds of brass fittings onboard a ship and the stuff works great and it is not near as messy. They sell small cans of it in auto parts stores where all the cleaners are. Will also remove paint and any residue left from stickers or whatever.
Micro fiber cloth and Brasso will work fine for tarnish and a minor polish. I would use Mothers Mag polish if you want a mirror finish though. Brasso can only do so much as the liquid has very large particles.
I would take apart the regulator for a better finish, but that depends on how far you want to go. I would either buy a buffing wheel that attaches to a drill from Home Depot or you can make your own with microfiber cloth and something to wrap it around that can be placed in your drill. Again, this would be for a mirror finish.
These are brass and stainless steel. They were unfinished coarse stainless and about 15 minutes with a buffing wheel on a drill I got a chrome mirror polish out of them with Mag polish.
This is a homemade buffing wheel with a micro fiber cloth ($8.99 100 pack) wrapped around a large drill bit.
If you want to go even further, you can use fine sand paper to basically reset the surface. 600 grit and move up to 2000 or even 5000 in increments. Then I use either brasso or Mothers Mag depending on the metal I am working with.