But if I understand what you've done, you're asking what clearcoat to use "on the whole piece" as one unit.....? Yes? Ordinarily, the chrome would be gloss, and the black would be semi-gloss........the woodgrain would be even a little more flat in appearance......so, a clear coat of any kind over the entire piece won't separate the appearances.......you know what I mean?
Here's a pic of one like yours that was done with a chrome paint, and then clearcoated (automotive clear....2K)....then it was masked and the black semi gloss was done.....then real woodgrain was applied in place of the brown paint.