Unfortunately, Google only offers 20,000 free songs without an option for purchasing more. Another alternative you can use is streaming from Amazon Cloud Player. I believe it's around 250k songs for $25/year.
If you listen to mostly MP3, then maybe consider buying some extra storage on Google Drive and uploading all your music there and downloading this app to stream it.
https://play.google.com/store/apps/details?id=dev.whylee.musicdrive
Since 19,000 songs probably wouldn't fit on your phone's storage anyway, what I recommend is to simply use Google Music and don't upload all the songs. 20,000 should be enough to keep you entertained for a while....
And yes, on Android, any media player will automatically detect any of your media files (unless you create a .nomedia file in the folder). If you really want to go the route of copying the songs directly onto your phone, I'd recommend you purchase PowerAMP. It's simply the best music player on Android. But again, 19,000 songs won't fit on the One's storage...unless they are all 1-2MBs each.