Start with Nachtstücke und Arien if you like Strauss's Four Last Songs or Britten's Serenade for Tenor, Horn and Strings. Also recommended: Royal Winter Music, Symphony No. 8 (both based on Shakespeare), Undine, and the Auden Songs sung by Ian Bostridge. Henze's stripped-down chamber arrangement of Wagner's Wesendonck Lieder is included at the end of the playlist.
Get this collection in one Spotify playlist: Hans Werner Henze - Reverse Chronological Collection (481 tracks, total time: 36 hours). Ctrl (CMD) + G to browse in album view. More links: song texts, work list on Wikipedia, AllMusic and Chester Novello; obituaries from Boulezian, Guardian, and Henze's publisher Schott Music.