I used some time ago a foobar skin named eole, which features a button which populate and start playing : 200 random tracks, 20 albums, one artist, random tracks from a random genre, random tracks from a specific genre (you can choose from a menu list when you click on the button)
This is really great when you don't know exactly what you want to listen, you can click on the button repeatedly, until something you like comes.
If you want to try the exact skin, to understand : http://alibalicou.deviantart.com/art/Eole-608641604
(if you just want to try, you can install foobar in portable mode, and follow the little installation instructions, it doesn't take much time.)
Of course, the reason of this topic is that it would be great to have a similar button on musicbee ! You can do something similar using the shuffle mode, or the auto DJ, but i didn't manage to make it as fast and easy to do than just pushing a button