Songs and playlists gone from new iPhone after accepting free 3 month Apple Music offer

I recently bought a new iPhone and restored all data from the old to the new one, incuding a part (20GB on my iPhone) of my itunes music (200GB on my iMac). These songs were included in the playlists I had synced with my iPhone. Now most of it (except the itunes purchaces) is gone from the new iPhone after accepting the free 3 month Apple Music offer that came with the new iPhone.

My itunes library consists of 200GB of music imported to itunes with hundreds of hours working on this, finding and incerting lyrics, album covers etc.

Now I'm afraid to turn my old iMac on (I work on the MacBookPro for months now), to protect all these years of work.

I want to keep my old playlists and songs permanently on my iPhone to be able to listen to my music even offline.

I don't mind cancelling my free AM offer, now or later.

What are the indicated steps to save my music and reload my songs ad playlists on my iPhone?

Thanks in advance for any answers!