I've never actually had a home server before so I cannot really comment on speeds, however if it's of any relevance it just took me 60 seconds to copy a folder of 330MB to it (2TB external HDD). I can stream music and films fine with no issue.
I use Samba for the file server, Transmission for a torrent box- it's really good, I can now access my torrents from any web browser (in my LAN) and can add/delete/start torrents- you can get it to work outside LAN although it's a little more work. And I use miniDLNA to share pictures/music/videos to all my devices, every time I add a new item the server picks it up automatically without needing to re scan the whole library. You can make an FTP server using ProFTPD, although I haven't tried. The OS for the PI is standard Raspbian.
There are tons of tutorials online as to how to do this, I have very limited knowledge of Linux yet managed to get it working, I haven't switched it off for about 3 months now