Alternative to iTunes?

Hello. I realize that this an iTunes-specific forum, but the functionality I am looking for isn't there:

1) The random and shuffle feature is not truly random, or if it is, there is something built in that it preferentially plays some songs more than others. I would like something truly random with a setting for minimal or no repeats so that my whole playlist gets played and not a few songs. As it is, I have having to FF through my own playlist because I heard too many of those songs on previous recent plays.

2) On the other side, though, I would like to be able to mark a few songs as high priority (favorites) so those get top-billing, and then it randomizes the rest. I can't see a way to prioritize and randomize in the same playlist.

I'd like to keep iTunes if it had this stuff, but I only use my iPod as a music player, so for me, there are only two most important functions: can it play music, and can it randomize the music without repeats, or with user-defined repeats. These second features aren't working so well.

If anyone has any recommendations, I'd appreciate it.

Regards,

leaning