I have a slightly more expensive version. I use a MacMini with the library on an external HDD. 4 TB worth. I have an Apple TV connected to my main TV and stereo system. I leave the Mini on all the time with iTunes loaded up.
Now, you can do the same thing by getting an Airport Express connected to your Stereo and set it up with AirPlay. then, just forward all the sound to that AirPlay and bam, all music from the phone is now going to the stereo. You can do the same with an AppleTV (probably better in the long run if you want to connect to your TV) and use the optical out on the ATV to hook up to the stereo. the ATV will need to be hooked up to a TV or some HDMI source to get set up, where the Airport Express does not.
All depends on what your final end goal is. I started with the Airport Express, and transitioned to the full MacMini as a media center driving 2 Apple TVs in the house. works wonderfully.