Need suggestions for streaming files to my stereo

You'll have to use a Flavor of Linux that supports ARM CPU's.  As for which one to use, I'll defer to thunder240 to answer that question.  Also, JRiver is Playback Application, not an OS.  JRiver is available for Linux.  If you're planning on using the Pi plugged directly into you audio system, you'll need the HiFiBerry kit.  Then, you would use an Application like JRiver to play music.  Many people swear by the Roon Player, but it's pricey at $119/yr or $499/lifetime.

If you're planning on just using the CCA as the Audio source, then all you would need is an Application like Plex, Kodi, etc to "serve" the music files to the CCA.  If you go this route, once the Pi is setup, you can run it headless; without a monitor.  You would use another computer, or tablet/smartphone, to control the Pi remotely for occasional maintenance, changes to settings, etc.  My Music Server is actually mounted on the wall right next to my router.  I use my main computer to control it remotely for occasional software updates, maintenance, etc.  Also, I use the LMS web-portal to control my Squeezebox Touch, which by the way, is sitting right next to me; it's easier than using the players own interface. To use the other Squeezebox devices located throughout the house, I use an app on my phone.

Thanks to all of you I now have a grasp of how the system works. Now that I understand it better, I thought of a few options. Please let me know what sounds best (or if it's even viable). 

1. Use a 7 year old Dell laptop that I forgot we had. Works fine but so may want to upgrade the wireless and Bluetooth. Drawback is if I leave it running for extended periods, it heats up and the fan engages every few minutes. 

2. Use a tablet connected to an external HDD that holds the music files?

3. Stick with the Raspberry option. 

Simplify your life, shorten your signal path, and improve your SQ. Keep all your music on a Mac mini, plug a decent DAC into it's usb, then plug the DAC into your amp. Done. Control it with your iPhone using the Remote App and/or your laptop with Screen Sharing. 

It has been mentioned here that many of the responses to the OP have not paid attention to the budget of $200. I, myself, admit to this error. But one must include the hardware cost of a computer. Like many of the newer (changing) technology with hardware associated with streaming digital it seems a more budget friendly option to just adopt newer software or even low cost hardware that attaches to a computer. The computer, itself, is a device that has limited life as a streaming device. HDD space, RAM and processor power, as well as software compatibility will become an issue.
I had wanted a separate device to stream my music. I want to keep ITunes and a computer out of the loop. Therefore, that is the reason I opted to go further with my budget to get a Bluesound Node 2.
At one time, I wanted to use an older MacBook Pro as an integral part of my audio playback, but alas it is too old and slow for this purpose.

Autre with your options I would ask myself which of these options would match your overall plans for a music playback system.