do i have to purchase music app to play my own music

You do not have to buy or subscribe to any external app or service to listen to your mown music (provided it is in the right format). The built-in Music app should work. See:

Import songs from CDs into Music on Mac - Apple Support

Import music from a computer to Music on Mac - Apple Support

Import songs from the internet to Music on Mac - Apple Support

Choose import settings in Music on Mac - Apple Support

Change import settings in Music on Mac - Apple Support

The Music app is simply part of the macOS setup. Are you asking if you need to *subscribe* to Apple Music? No, you do not. Just put those tracks wherever you want and add them to your Music.app's Library.

You might have to decide how you want the app to handle them. I believe by default they are copied into your user Music library. This does not move but copies. In other words you will have two copies. It is OK to not copy them to that folder. For example, I have all my tracks in a folder on an external drive. See Music's Settings>Files tab.