Copyright law and dulcimer music

Hey all this has been something I've been struggling to understand and I'd love some resources that could help me.
Can an arrangement to a public domain song be copyrighted? If I take a song from the 1800s that has a known melody and chord progression, and plug it into a dulcimer I would imagine this would not be anything I own, but I have read some confusing stuff on the topic. 

Also, because guitar chords to songs I like to sing are so easy to find online I often just take the guitar chord progressions and strum them on dulcimer. Let's just take for example the chord progression of I–V–vi–IV if it was in D that would be D A Bm G but a D chord could be 000,002,200,034,430,234,432, etc etc so does choosing which 'expressions' of the chords make it a unique piece of copyrightable music?