When you watch the travel shows, you see in Grieg's studio, his treasured piano: which Rick Steves actually got to play a little bit. Sibelius, by contrast, they show the restaurant where he used to hang around with his buddies. So what did he do, slip the house band his drafts on Tuesday nights, along with a big tip? (Classical Destinations TV show, Sibelius episode). I've gotten 6 Sibelius LP albums from the charity resale shops lately; all the doctors are dieing off and their children don't need any PVC, thank you. Besides several un-distinguished symphonies, there is an album of short orchestral pieces with titles from Finnish mythology. No piano music. So I'd say start with Wedding at Trollhausen by Grieg, for a breath of air from the frozen north. It is on my list of music to do in my life, about entry 800 or so.
Why not just pick up the Dover collection and have a play through? It's opretty cheap and fine for exploration.