I am trying to find a free music player that has the feature to select a section of a file to seamlessly loop infinitely. Like, it plays the song beginning to end, then starts again at the looping point instead of the beginning.
go for this good one, Winamp
How can one make WinAmp do that?
On the front face of Winamp if you hover on the buttons it will tell you function it does.
This probably isn’t exactly what you want, but if nothing else there’s a plugin for Spicetify (a tool to modify the Spotify desktop app) called LoopyLoop that adds this functionality.
I don’t use Spotify, unfortunately. Ideally, I’d want an app where I can use my own mp3 or wav files.
Spotify does support local files! It can be a bit of a hassle since you need an account, but you can definitely point it to folders on your PC. Though, it seems like others have already suggested some better options for local players 
.
Musicolet free version and jetaudio
I think VLC can do this! Just hit play, then set your start loop point by pressing the A-B loop button. When you reach the end of the section you want to loop, press it again to set the finish point. I’m not sure if it’ll loop from the end without that finish point, though. After that, it’ll keep looping that section until you decide to change it.