Hey nita202,
Thanks for the update. Any music you had on your Mac before you signed up with Apple Music may still be on your device. By default, your music is stored in Home/Music. You can navigate there in Finder and either use the search option there or look through the different folders to locate your music. If you cancel Apple Music, you should still be able to access your music there.
As for buying music from the iTunes Store, it is a little different since Music was introduced, but only a little. Follow the steps under “Buy music from the iTunes Store in the Apple Music app on your Mac” from this article for info on how to do this:
Buy music from the iTunes Store
If you do run into any issues with connection speeds, the steps here can guide you on what to do:
If you can't connect to the App Store, iTunes Store, or other Apple services
We hope this gets you moving in the right direction.
Hope you have a great week.