Everybody loves The Planets. Well, more accurately, everyone knows Mars and Jupiter, and probably wouldn't recognize anything else as part the suite even if you told them the name of the movement was "Saturn" or "Venus". But pimping Uranus (ha ha) isn't the point of this post. One of the things people don't know about Gustav Holst is that he was a trombone player and did a lot of non-orchestral composition, much of it for wind or military band. And unless you're a band geek like me, you probably won't be familiar with any of his other literature.
One of Holst's contemporaries was a fellow Briton named Edward Elgar. Elgar is best known for his Pomp and Circumstance marches. (You already know the first one because it's played at every single graduation ceremony in the Anglosphere.) While the marches are quite good, I'm actually a bigger fan of his other compositions - especially his Enigma Variations, a cryptographic musical love letter to his family, friends, and (in the true hubristic spirit of the 19th Century artist) himself.
Unlike Holst, Elgar never wrote directly for wind band, but his compositions are relatively simple and have been transcribed for (and largely played by) wind ensembles. I'm going to exclusively use band arrangements for both composers here. I encourage you to find orchestral versions and listen to those as well.