The two main commercial professional-grade music-"engraving" systems
are Finale and Sibelius (they used to be discussed extensively at the
newsgroup rec.music.classical before it fell victim to all sorts of
spamsters and pranksters), and I believe both of them have simplified
versions intended for beginning music students doing their homework.
I got into Finale a long time ago because it was the one sold at the
Juilliard School's bookstore (I have no connection with Juilliard!) at
a steep academic discount, and over the years it's become somewhat
simpler to use and considerably more feature-packed. (Their website is
www.finalemusic.com.)
I've never looked around for music freeware. No idea how sophisticated
(and reliable) such products may be.