Is a coin finish, or brushed finish, essentially in the white aka no finish?

This Alfred London I'm fixing up was old gun, deep rusty brown patina, and I wouldn't think it was color cased. If that's right, what would be an acceptable finish after the rust is cleaned off. Since some things needed to be blued, based on other English SLE's I've seen, I went ahead and soaked everything in rust remover. The parts not yet blued are grey, which is fine, but dull.

My thought is that just a slight bit of shine would be nice, and perhaps inking the engraving just a bit. I'd appreciate some perspectives on brushed and/or coined finishes. This is not a restoration endeavor; just putting a gun back in use with a decent appearance.

Thank you.