I like the “mini” version of the iTunes player but no matter where I put it I feel like it always gets in the way… I stumbled upon this option by mistake but now I can’t live without it.

All you have to do is right click on any free space on your taskbar go to the “toolbars” menu and select “iTunes”. I think you have to do it while iTunes is running, but maybe not. Also, I’m running iTunes 4.8 but it may work in other versions.
From now on (unless you unselect this option) whenever you minimize iTunes you’ll get a mini player in your taskbar!