Got a CVA mountain stalker yesterday and it has some rust in the barrel.What's the best way to go about cleaning it out?

You can use most any toilet cleaner that removes "iron stains" such as CLR, or something thicker like Naval Jelly. The thing to be aware of is that the blue finish on the barrel is also iron oxide and if ANY rust remover at all gets on it you'll have shiny splotches. You can wrap tape on the front 6" of barrel but still be super careful and then wash everything off with soap and water when you are finished. Also, a brass brush works well for scrubbing the rust in conjunction with a cleaner.

I have cleaned up several barrels from super bad rust , I use 4-0000 steel wool on a brass brush soaked with PB Blaster , or liquid wrench clean till no rust is seen then use a cleaning rag on same brush till no rust is seen on rag , will take several hours to complete but worth the trouble and work to restore like new .
Have fun .

I usually use a brass bore brush and WD-40 to get the majority of the rust loose, then follow it up with alternating wet/dry patches until the patches come out clean. After that, I run an oiled patch down the bore to keep it from rusting again while it's being stored. The only thing I'd be cautious about with a muzzleloader is not using too much oil; if you leave a pool of oil in the breech, it can wet your powder to such an extent that the gun won't fire. For that reason, I usually lean my muzzleloaders in a corner muzzle down for several hours after cleaning to make sure any excess oil/solvent drains out.

Give Butches Bore Shine a try.

Al