Worth saying that this is typically the type of project which is handled by a professional A/V integration company, not the DIYer type. But, you do have a number of possibilities, which is far over-reaching without knowing more about your overall budget.
1. Generally every room needs discrete amplificiation. It sounds like you have a room with surround sound (A/V receiver required) and 5 stereo zones for audio only.
2. The 5 stereo zones would typically be fed with a multi-channel amplifier, like this one:
Speakercraft BB1235 12 Channel Big Bang Power Amplifier | eBay
That provides up to 6 stereo zones with discrete amplification.
3. The hard part is that in front of the amplifier you need an analog stereo matrix switcher, which is available, but generally hard to setup/program by end users.
You have things like this:
Amazon.com: Speakercraft MZC-66 Multi-Zone Audio/Video Amplifier Controller - Shelf Top: Electronics
Which include source selection and amplification... Likewise, complete packages like this:
Amazon.com: CHANNEL PLUS MDS-6A KIT 1 6 Source Multi-room Music Distribution Kit #1: Electronics
...are available. I'm not familiar with these types of kits and if they offer RF remote integration of any type.
4. Consider Sonos for the different zones. Most people really like Sonos, and you can buy either five amplified Sonos players or a multi-channel amp (like listed above) along with 5 Sonos zone players. I believe you can access your entire digital music library as well as share analog inputs and it comes natively with iPhone/Android controlability built in.
5. The most typical method of doing this, as a consumer, is putting volume controls in every room and simply running things manually. It isn't that convenient, but it does work. It's a lot less money.
6. The main surround zone needs a standard surround sound A/V receiver. Pick from a long list which matches your budget. Get speakers which are appropriate to the room including a subwoofer. To get audio into the A/V receiver use the HDMI connection from your sources and/or the digital audio connection. Save the analog audio connections for your distributed audio.
7. Custom solutions, like Control 4, Crestron, and AMX also provide a very high end solution which must be custom installed. They are pricey, but they won't really give you any headaches over the long term. I've had my Crestron home system installed for about 7 years without a single headache. Similar situations with my customers. About $700 for the controller, $600 for the audio matrix, then the amplifier, speakers, and installation/programming time. So, not cheap, but extremely reliable.
As said, there are many ways to approach this, but your budget will figure a great deal into the final quality of the product. At $300+ for in-ceiling speakers, you have the budget for a very nice setup, and it may be worth it to hire a company locally that can simply set everything up for you properly and provide the best product for you. This is up to you.