Making an assumption that THIS gun has no collector value- because rebluing a gun will wreck that-
Bluing of steel is controlled rusting- black iron oxide instead of red. Naval Jelly will strip bluing in seconds- it contains phosphoric acid.
Bluing will not cover bad surfaces- it just changes their color- they still look bad. For a hobbyist, I am going to suggest wet-or-dry sandpaper, wet with light oil. A gunsmith would use power tools, such as a felt wheel, flapper wheel, etc. But you can do a nice polish if you take your time using just hand power. Start with 120 grit, wet with oil, use the "shoe shine" technique. pits and grooves will collect black gunk to show where you need to keep polishing. Then clean it off, move up to finer grade, repeat, and then to a finer grade. 400 is probably fine enough for what you are doing. You CAN push it higher. For a final polish on some steels, I use white jeweler's rouge on a felt wheel or bob, but that is pushing things a bit.
For FLAT surfaces, use a flat backing block to prevent rounding sharp edges.
Rather than a cold blue (cold blue is like kissing your cousin- better than not getting kissed at all, but not much) why not do some research on rust bluing? Simple process, not a lot of methyl ethyl killya used- and it gives a nice finish. It DOES take time.