Foobar doesn't have to take up the whole screen - you can configure it however you want. Here are a couple of examples (not mine)
Any mine when it's minimized
I still have general playback control of the application even when it's minized. I have even installed a remote control server for foobar allowing me to remotely control the program from my other machines. You can search your libraries, modify playlists, change/skip songs, queue songs, etc. using this tool.
You should also be aware that a default installation of foobar isn't pretty - it looks like this
The configuration is all up to you with Foobar but you may have to RTFM.
I don't use iTunes anymore because it's pretty closed off. I like the ability to add support for fuctions to the application easily. Flac is not a supported format in iTunes and ogg support is pretty crappy on the Mac side. I refuse to go with Apple lossless because I play my files on Windows, Mac, and linux using Foobar, Cog, and Rhythmbox primarily. I don't have to duplicate any of my audio library because it all sits on my fileserver that is mapped by all my other machines in the house.
You stated that you wanted an alternative for your music so I assume you only care about the audio support. If you want any video support at all then don't look at foobar - it will never be added. The programmers have made it very clear that this is an audio management tool and not an all purpose media player.
Take a look at this wiki to get an idea of the types of functions you can add to foobar.
http://wiki.hydrogenaudio.org/index.php?title=Foobar2000:Components_0.9