E10.
It is E when downloaded, but in a large sense it's close minded to think that it would stay that way. A majority of songs would fall under E10, giving the notion that this game is aimed towards more mature players, and that the songs are for a generally older audience. Dance Dance Revolution X2 is different from Dance Dance Revolution Disney Grooves, which is rated E while Dance Dance Revolution X2 is rated E10. This isn't exactly the same situation because of course it brings practically all the songs (minus downloadable content). It's stupid to think someone would download osu! just to play Peter's tutorial though.
It is also an online based game, so an ESRB rating wouldn't work too well. If the game was sold in an arcade machine or console game (even PC, sold in stores though) it would be different, and it would most likely have songs on it.
In a general sense, you need songs to play osu!. Most would fall under E10, and using a song filter by rating of language used would eliminate the need for the T or M rating.