iTunes and Apple Music

I've just bought a new 24" iMac, as my old iMac was too slow. When I open the Apple Music, my iTunes songs that I have previously purchased are not there.

The only answers I have found so far, are to subscribe to Apple Music or iTunes Match. I done feel I should have to subscribe to either of these, just to access songs that I have already purchased. Any help would be greatly appreciated.

Thank you