Wikipedia (1865-1957) [Finnish. Romantic/Modern.]
If you're just gonna listen to one: Valse Triste
Background
People haven't always taken Sibelius seriously; he had many critics during his life. Why? Well, he continued to write music in a solidly Romantic and nationalist style, even as the arc of classical music was following the Second Viennese School into modernism. His music can be emotionally sweeping and maybe a bit schmaltzy. But if that's your style (like it is mine), then you're all set.
Orchestral
Sibelius' symphonies (seven of them) are the core of his work, and are probably the most commonly performed of his compositions. He also wrote many symphonic tone poems, many of which are based on famous Finnish poetry. He wrote only one concerto, for the violin. It was his desire to be a performing violinist as a young musician, but when that didn't work out, he turned to composing. The Violin Concerto is a well-established part of the violin repertoire, and reflects his fondness for the instrument. (Hilary Hahn will be in Seattle on 4/25 & 4/27 performing this work with the Seattle Symphony...)
Violin Concerto
Symphonies: Five | Seven
En Saga (tone poem)
Finlandia is probably one of his best-known works; it was written to rally the Finnish people, who were under Czarist Russian rule. The piece is quite dramatic, but the last theme is very gentle (from 6:10-8:15), and this music is also used as a hymn. That music was also featured in the film score for Die Hard 2: Die Harder.
Vocal
Hymn to the Earth
Oma Maa (Our Native Land)
Sibelius created a few large pieces in the mid 1920s, but pretty much stopped composing after that. Some sketches of an 8th symphony have been found, but for the most part, Sibelius spent the last 30 years of his life not writing music at all...
