I do quite a few tracks with public domain material. Mostly Xmas songs and now I started variations of children's songs.

I don't register them with the copyright office. If I did, I'd register it as an SR (sound recording) and list the original composer (if known).

When these tracks are registered with ASCAP, there's a line that includes the original composer that needs to be filled out. If it's not known (or questionable) it's listed as "unknown" like "Green Sleeves".

There are websites that list public domain songs in alphabetical order. You'll find several if you Google.

Best, John smile