I am fond of 20th century Estonian composers. I know that is a slightly esoteric set.
One of my favorites is Arvo Paart, to whom I have been listening since mid-1980s (my first job!), in particular Tabula Rasa (possibly his most accessible piece, if you're starting. Here's a New Yorker article about him). I came to Paart by way of Philip Glass (who has a new autobiography out). I find the minimalist music to be clear, and when you listen, far from simple. Another is Veljo Tormis (whose Litany to Thunder is a more vigorous piece).
Right now I am listening to Heino Eller who I heard this morning. This 1917 piece is a little more lush/lyrical than what I heard, the 1953 5 Pieces. But its a start.