I recommend the "deep cleaning" process for both your barrel and your choke tube. Many shooters never thoroughly clean their shotgun barrels and when a gun is used for upland hunting, waterfowl or even clays, it will still function well enough to meet their needs. Because we use a shotgun more like a rifle and because many of us pattern our guns now, it's very easy to see the difference when you shoot a clean barrel.
I advocate starting out with a deep cleaned barrel and then try your gun, choke and shotshells without cleaning between shots, until your patterns degrade. That way you'll know how your gun shoots best...with a clean barrel...a slightly dirty barrel...or a very dirty barrel. If you clean between every shot, you'll never learn if your gun shoots best with a slightly dirty barrel, for example.
When you switch shotshells or chokes, I recommend a thorough cleaning again. A thorough cleaning means using some solvent, a good brush and some patches but is not as extensive as the deep cleaning process.
There are guidelines on OG for barrel polishing if after a deep cleaning you're not satisfied with your patterns and want to see if that will help.
You can read the deep cleaning guidelines that I recommend by clicking on the banner below and then reading the article "Cleaning a Shotgun Barrel"
Thanks,
Clark
