If the iTunes Mini-Player option in iTunes doesn't quite serve your iTunes management, Cockatoo from Intuitive Code might be for you. It lets you easily control the iTunes music player.
You can control iTunes from its interface and also from the Dock (by right-clicking the iTunes icon), but Cockatoo provides other options. You can have it "sit" on either the left or right hand side of your screen. Move your mouse to the location you've chosen, and Cockatoo springs into action. (After first installing it, the left hand side of the screen is the default location).
When Cockatoo launches, it automatically launches iTunes if it's not already opened. Info about the track that's currently playing is shown. Cockatoo also lets you navigate the track and volume controls and select the next or previous track.
Cockatoo does what it's supposed to do. The iTunes Mini-Player serves me just fine, so Cockatoo is a bit redundant for Yours Truly. However, you may feel differently.
Cookatoo costs US$5.99 and is available at the Mac App Store. It requires Mac OS X 10.9 or later.