A trick I learned for dents that both ding the metal and raise a little ridge is to use something very hard and polished to push the metal ridge back down before generally polishing. It won't get rid of the ding but it helps reduce the remaining "divot" in the metal. To do this on some stainless you'll need something VERY hard. The best way to make such a tool is to get a good quality philips screwdriver and then using some fine wet or dry sandpapers followed by some polishing compounds polish the sides of the blade to a mirror shine. Do this in a drill press or hand drill with the tip end in the chuck. You'll be wanting to use some rubber tubing on the tip as a second handle for the forming anyway so don't worry about polishing all the way to the tip.
To use lightly oil the driver blade and with the gun held in a vise with padded jaws firmly push the polished driver over the ridge to push the metal back down into the hollow. With a bit of work and a few passes you'll be done.
A nice polish job always looks better when the straightness of the cylindrical shapes and the flatness of the flat areas is enhanced. For the cylinder and barrel wrapping the sandpaper around a bit of pop/beer can side metal will provide a nicely rounded and supported polishing tool that will help remove the deeper scratches while maintaining the sharp edges and basic overall trueness of the barrel and cylinder. For polishing the flat areas to remove marks and scratches you want to use something flat to support the sandpaper. Obviously there's some areas and inside corners you'll need to use just some folded over sandpaper but try to do most of the work with the paper supported either with the pop can metal, a flat block or stick or with various close fitting tubing, drill bit shanks or other shape holding supports for the sandpaper. Doing it this way will really help avoid rounding over the sharp accent edges that can make the gun look like a half used bar of soap if overly done.
For paper I'd suggest starting with 400 wetordry if there are any deeper scratches. This will help remove the scratches but not cause a big amount of metal removal. If you start with a more coarse grit it will remove too much metal which may begin to compromise the safety of the gun. Then move on to 600 grit and work out the texture left by the 400. If the scuffs and scratches are minor and not noticably cut into the metal then start with 600 instead. Sand until the surfaces have an even look to them from the paper. Then go to 800 or 1000 to do the same with the 600 sanding marks. From there jump to 1800 or 2000.
Now if you've been good and there really isn't anything much that is actually down into the metal you may well be able to jump right onto the 800/1000 grit option and get a nice job of evening out the surface appearance. Basically if you can notice some or a lot of the marks when you drag a fingernail over it then you should start with the 400 or 600. If the fingernail can't feel the marks they are superficial and a light polishing with the 1000 and then onto the 2000 will prep the surfaces for the final polishing for a mirror finish.
All the sanding stages should be done "wet" using water with a couple of drops of dish soap for the first couple of grades. For the 800/1000 and 1500/1800 grits I like to switch to mineral spirits. But when you use the mineral spirits you'll want to use protective gloves to avoid the long term skin contact. Or at least use a good barrier cream on your hands for this step.
You'll go through a lot of sandpaper doing this, especially with the superfine grits. Don't skimp on the paper, use it for a while and when you notice it's not cutting as well then toss it and move on. The only exception is with the last final grit. Using it past it's most effective point will dull the paper and make it produce a smoother finish which is a nice transition to the final mirror polishing with the mag wheel or stainless buffing compound step. Or if you're after a more "flat" sort of brushed look then you may want to put that on in the final steps with some fresh 1800 paper or even go down to some 1500 grit for a slightly coarser brushed look.
At that point you may like the buff sort of matt sheen it'll have. If so just work the paper so the sanding lines are all in line for a nice even look and call her done. Or you can move on to some mag wheel polish to bring it up to a mirror shine. If you do this I would suggest you do most of it by hand again using cloth buffs wrapped around the same supportive backings as the sandpaper for the same reasons for the barrel and cylinder. Only a light final buffing on a cloth wheel to finish it should be done if you want. But really the entire job CAN be done without ever using any electricity. You'd be surprised at how a cloth power wheel charged with polishing compound can dull over a nice crisp accent line if it's used with heavy pressure for too long.
All this will be much more work than jamming it onto a buffing wheel or using a pour and shine solution but it'll do far more to restore the look of the gun and remove much of the handling damage done over the years. There's no doubt that the Flitz mentioned above will shine up the metal but it won't remove marks that are more than very light scuffs. Anything deeper will still be there. At no time should you give in to the idea of using a Dremel tool on your gun for this refinishing. That would ruin it due to the waviness in the surfaces that would occur due to the small footprint of the wheels.
The wetordry sandpapers are all stocked at any decent autobody supply outlet.