The best solution is to remove the pits entirely. Any other approach will be a half-measure at best and will be something you probably won't be satisfied with in the long run.
Most competent gunsmiths should be able to take the metal down just enough to get under the pits. I have done this myself with slow and judicious use of a belt sander, but it's not something I'd recommend to a novice. You can do it yourself with sandpaper taped to a sheet of plate glass but it is a slow process.
The only problematic area might be the serial number. Depending on how deep the pitting is, the s/n might need to be deepened or re-engraved.
The alternative is the quick and dirty method. Have it sandblasted (bead blasting won't be aggressive enough) and treated with something like naval jelly or some other rust remover to remove the oxidation at the bottom of the pits. Otherwise it will just return sooner or later.
Then have it coated with Gunkote or something similar, to prevent future rusting. I wouldn't waste the money to have it plated if you aren't going to polish out the pitting.