This all depends on what you want to do and how much you are willing to spend.
I have a HA system called Control4 which I use for HVAC, lighting, blinds and fireplace. You can also use it with media, security systems, etc. There are apps for iOS so that you can use iDevices to control the system or you can get dedicated touch screens and remote controls.
To distribute the video signals you need a matrix switch - these can get VERY expensive and (obviously) wiring from your central switch to all other spots - I think you can use CAT5 for this. But there are other ways to distribute the video and audio such as Sonos (for audio), AppleTVs, TV extenders (like an Xbox360)
Are you sure that you need centralized distribution of everything? It is usually much cheaper to just put all of your sources (like AppleTVs, cable boxes, BluRay players) at each TV since high-end matrix switches cost a few thou. But Monoprice has 4X4 matrix switches for a reasonable price of about $300 including remotes, etc. IMHO the main reason to do distributed video is to have whole home distribution of video content from one central place. But there is less need for that if you content is coming from the cloud in the first place.
There is generally one controller that can handle everything but you will need one main controller to drive the whole system and you may need smaller "slave" controllers at some of your audio or video endpoints as well depending on what you want to do.
For A/V (and I really do very little audio only) I have a SageTV PC server in my basement. This is connected to two HD cable boxes, one SD cable box and three OTA tuners. I have several TBs of hard drive space with ripped movies and previously recorded TV. At each of my 6 TVs I have a SageTV extender that connects to the server via ethernet and allows me to watch all of my video content, or play audio. With such a system I can start watching a recorded show (or movie) in my basement and continue watching in the kitchen or bedroom. This Sage system is not part of my HA and most HA enthusiasts want to distribute via video switches rather than ethernet for some reason.
These systems can be very expensive and many of the systems are only sold and installed through dealers and you can't always do as much as you want without calling a dealer. Crestron is another player in this space that is very high end and used in many high end office installations and with them almost everything is done through a dealer.
I used Control4 and they are somewhat DIY but you still need a dealer to do a lot of things that I would prefer to do myself. For example if you use C4 for media and you want to change the BluRay player that you have in the system then you have to call the dealer to have him install a new driver for your new BR player. IMHO these companies are still struggling with trying to figure out whether they are hardware or software companies and also with how much they allow the user to do without a dealer. The introduction of the iPad really caused issues as they sold dedicated "dumb" touch screen controllers for $1500 or more. The iPad comes along for 1/3 the price and what do they do? Do they develop an app for the iPad? If so then how do they monetize it?
To give you an idea of costs - I would think that there are very few Control4 installations that are less than $10k and you can easily go well beyond that. And Crestron is more expensive than Control4. I believe that Control4 light switches/dimmers cost about $100 each plus installation. The main control unit costs from $500-$1000 depending on which unit you get. And the sky is the limit.