I love using stainless steel because I have always hated rust and especially when used for dropouts, fork crowns and brake bridges. It means your paintwork doesn’t get damaged. I found out how to polish it up from the instructions given by Darrell McCulloch of Llewellyn bikes fame and you can do no better than reading: http://www.framebuilderscollective.org/polishing-stainless-mcculloch/
I used to polish the parts after completing the frame but, as McCulloch, I now file and sand the parts to at least 240 grit emery paper before building the frames. It is much easier to get in all the recesses before the frame is assembled.
You need to file off all the surface imperfections first otherwise they will show through, the buffing will make any pitting stand out more. Size and grade of file depends on size and roughness of the part in question but often a small fine 4 inch (100mm) file is enough followed by some needle filing to get it really smooth. I use the Vallorbe Swiss files for preference and as Mr McCulloch says the newer the files the better they work so I keep the newest ones for this purpose. I then move onto sanding with 25mm emery cloth strips. I find 120 grit is a little coarse but is still OK to start if you follow up with finer, Darrell McCulloch recommends starting with 80 grit, 240 grit, then something like 320 grit then 400. Thus far I have always then moved on to the buffing stage, though it has to be said I have often had to back pedal and use emery cloth again so perhaps I should be following the advice and using 1000 grit before the polishing phase. Additionally I did speak to Darrell McCulloch’s wife at Bespoke 2016 who told me he finished by sanding in one direction which I will have to try. Axminster do small packs of different grits which are ideal.
I often use a rotary tool with a miniature sanding disc to speed things up but there really is no substitute for filing and hand sanding. Dremel do do various scouring buffs which work a treat but last no time at all and are so expensive as to be impractical. I personally have not found the larger scouring buffs (as used on electric drills) to be of much use, these are the type that look like scotchbrite. You can however obtain small polishing buffs for use with the polishing compounds (see later) for rotary tools which are useful for small recesses, though they do not last long. If you have not filed or sanded enough after polishing it will be obvious and you will have to redo the area again. A stainless steel polishing kit is made by PoliCraft widely available including from Halfords.
It consists of an arbor and three grades of buffs and polishing compounds to be used sequentially. The kit is used on an electric drill. Recently I have purchased a bench grinder (reviewed elsewhere) which can be converted to a polishing machine to try and speed things up. The seller, Metal Polishing Supplies, supply a complete range of polishing sundries though various engineering suppliers supply similar kits and consumables.
I have not found that using a large buffing mop like this speeds up the operation a great deal as it does not get into the recesses very easily so I still end up using the smaller drill or rotary tool mops for the detail finishing. The electric polishing is messy and is best done outdoors, a face mask helps prevent you ending up with a black face. Polishing mops will only remove the lightest of scratches so you cannot really polish out poorly prepared metal, the polishing will then simply highlight neglected pits scratches and imperfections.
Darrel McCulloch does not polish stainless tubing, only lugs and dropouts etc. The reason given is they are thin enough already and it is not worth risking thinning them any more. I have dabbled with polishing both XCR and Reynolds 953 tubes and I found it is difficult to polish out the scratches without being too aggressive leading me to abandon the process before reaching the point I would have ideally been happy with. 953 tubes are especially scratched from the belt sanding done on them before despatch and I will be asking them in future if they can send them un-sanded. Reynolds will offer mirror polished 953 tubes but there is a price premium which would make it much more cost effective to polish your own. 953 fork blades do polish up reasonably well probably because they are supplied un-sanded with the natural oxide coating.
Stainless steel polishing takes a lot of time and patience and therefore well suited to those who are not building a frame to time or price constraints.
Regarding maintenance I have not found that metal polish particularly enhances the finish after the buffing process. I also have found that a bicycle polish such as the one below, maintains and restores the shine admirably.