1) a blued finish is pretty to look at but not very protective. The metal is usually polished before being blued so blued finishes show scratches easily. It looks great, though, for show pieces.
2) parkerizing produces a rough surface finish that is thicker and protects better than blued since the rough surface retains oil better than blued. The non-reflective nature is also preferred for serious work.
3) moly/teflon finishes are essentially a paint that is baked on. The flat or semi-gloss black one's look very much like a parkerized finish. They wear about like a good parkerized finish but protect the metal much better than just about anything else. They also have the advantage that they are easily, and cheaply, applied at home using nothing more exotic than a $20 airbrush.
Stainless steel doesn't need a finish, obviously, unless you want to cut down on reflections and then it is usually bead blasted to give a matt look. It can also be blackened through a chemical process or you can paint it with moly/teflon finish. Stainless is heavier and, generally, harder than high carbon steel.
Interestingly, though, when used as a barrel material, it doesn't last significantly longer than one made with carbon steel.