Where can I find a complete legal list of songs that are in the public domain?

I don’t think you will find a “complete list” anywehere, but yest, songs that are Public Domain can be played and sold without royalties. The only one that comes directly to mind is “Amazing Grace” and maybe some nursery rhymes.
Here is a list of some

Like @Judi says, there is no complete list. For one thing, something that is public domain in the US might not be public domain in the UK. As far as music in the US is concerned, however, anything published prior to 1923 is now in the public domain (whereas anything unpublished is protected by copyright for a minimum of 70 years after the death of the author).

Here is another site that might be useful when trying to determine whether or not a song is in the public domain. Always exercise due diligence in confirming that the information these sites provide is accurate. If it is, then you are free to record and sell new versions of those songs as well as perform them live.

Important note: Only the songs themselves are in the public domain, not recordings of the songs. The latter remain under copyright. This is why anyone can freely play a Beethoven symphony, but no one can freely replay the von Karajan recordings thereof.