I have learnt a lot from The Letters of J.R.R. Tokien. You have to do some fishing around, but there are gems hidden in it.
As a Tengwar exercise, The Road Goes Ever On (a song book with Donald Swan) can be fun, also these are "canonical", "Tolkien-approved" songs. He even made the melody of Ai! Laurie Lantar Lasse Surinen! himself, as a sort of Gregorian tune.
Of course, the Silmarillion and Unfinished Tales are both important works, both containing stories from the First to the Third Age.
If you want all the tragedy of Turin's story, read The Children of Hurin for all the wonderful details.
If, like me, you like Pauline Baynes' illustrations (which are also "Tolkien-approved"), I urge you to have a look at Bilbo's Last Song and The Adventures of Tom Bombadil (The latter also contains more written information).
I think that's mostly it.