For Classical two magazines i used to read (for free)
American Record Guide
I liked American Record Guide as it had broader coverage, and also had regular articles doing an 'overview' of a particular artist, or type of music from an artist. Such as Puccini Operas. Or all Beethoven symphonies, and in them one could read a cross section of many good choices to buy. I loved the overviews. This magazine is often available at larger public libraries, and for Classical mavens, well worth searching out to check out the overviews in past issues.
And
Fanfare.
Fanfare was rather specialized, as they only reviewed stuff they got as demos. So plenty of small lables, but nothing from the majors.
I have no idea if they are still published.
For Jazz, Downbeat has reviews, but I liked Jazz Times reviews better.