I hope this message finds you well. I am a licensed IP attorney with over a dozen years of practice experience. It is a pleasure to assist you today.
The answer to your question is. optimally, you register both. At the moment, you own the rights to the song. So, you can copyright the lyrics and the notes relative to the song (costs about $30 on the US Copyright website using their on-line filing system). You can also separately copyright the sound recording. As a matter of fact, you should copyright the sound recording as well.
Technically speaking, if you commissioned the artist to sing your song, then you own the rights to the performance, unless there was an agreement to the contrary. That said, I have found that the best way to handle this is to offer a carrot to the artist and state (contractually) that you will give them a 5% (or whatever number you deem fair) royalty on sales of the performance but you are going to file the copyright for the sound recording under your ownership only since you commissioned the work and own the rights to the song as a whole.
This step typically satisfies the artist and it also helps you avoid legal trouble down the line if the song takes off. You can file online for protection of the song recording too if you have it in a wave file format.
Let me know if you have any other questions or concerns. Please also rate my answer positively (THREE OR MORE Stars) on the ratings bar on your end so I can receive credit from the site for my response.
Best wishes going forward!