Hi HU,
First on stones, IF you have a local machinist or industrial supply store, it may be cheaper to buy stones there even though the list cost is usually a bit higher than ordering them. However, shipping costs can make them way more expensive unless you order a bunch of stuff at a time.
Stones give you a much, MUCH flatter and precision surface in many small areas of lock parts, where that is super important.
I looked up the McMaster Carr stones and I could not find THE stone that I consider essential to polishing the faces of sears and full cock notches. That stone is a 4" length, 1/4" three square or triangular Hard Arkansas stone (also small stones are sometimes called files). The triangular shape and size is perfect for the full cock notch. DON'T waste your money on the 6 inch length stone in the following link, though. Using this stone with oil to do just a few strokes on the surfaces mentioned will bring surprisingly good results on locks used without set triggers.
Triangle Arkansas File (sharpeningsupplies.com)
I haven't used the company from the link before and this one following, though I find the FINE grade stone in this link interesting if you have to cut metal, say an especially rough or gouged full cock notch.
Aluminum Oxide 4" x 1/4" Triangle File (sharpeningsupplies.com)
I normally buy Norton India (aluminum oxide) stones in Fine and sometimes medium, depending on what I'm dealing with for gun work.
The following article is excellent for information on oiling and especially FLATENNING stones, which you will have to do from time to time, especially on aluminum oxide, Norton India Stones that are used often on hardened surfaces.
Oilstone | Flattening | Cleaning | How To | Woodworker's Journal | Ernie Conover (woodworkersjournal.com)
Gus