Throwing some thoughts out on this one...
Traditionally, this type of process is done using hard wired systems.
Speaker wiring is pulled to each room where audio is wanted and speakers at setup.
Newer concepts, such as Sonos allow for wi-fi to be utlized to transmit compressed audio to a receiver in each room which decodes the audio/video and plays it back through local speakers or even to displays (AppleTV or WDTV).
I am not sure of your entire FM transmitter concept. Actually, I'm pretty sure you are dreaming on that one. FM transmitters I don't think can be powerful enough to go beyond about ten or twenty feet because of FCC compliance issues. A long range FM transmitter is called a radio station, and you would likely need some very expensive permits and equipment to set such a thing up. BUT! I am not an expert on this and obviously there are people who are really into setting up local radio stations, and likely websites dedicated to such things, which would be able to answer those thoughts of your far better than most A/V guys can.
The downside of any FM broadcast is that it is entirely a one-way setup. You have to go to your main location, start music playing, then you can access it from other points, but you wouldn't be able to pause, stop, or skip tracks you didn't want to hear. No control at all.
A real monkey wrench in all of this is your budget.
Cheap audio gear can be bought used, via eBay, amps can be had for not a lot of money, and switches and the like can be found. But, to get control, and to utilize newer technologies such as wi-fi to get your audio moving around typically requires a more cohesive integrated system which plays nicely with multiple components.
But, if your budget doesn't afford you the new gear which allows for this then you may have a really hard time trying to achieve what you are looking for without going to FM equipment which is well beyond my scope of capabilities or recommendations. The fact that you go into A/V stores and there is absolutely nothing for FM broadcasting for wireless, beyond the 10' range car iPod adapters indicates that there are some real hurdles which are a part of FM broadcasting.
If you throw in the need/requirement for video to multiple locations as well, I would lean more and more towards an AppleTV/WDTV type of solution.