I'll start by saying youre in luck as a Verizon customer. Verizon and Comcast are the most lenient with the way they use DRM. That gives you some more options for getting recordings around your house. They could change that at any time, and your recordings would only play at the location they were recorded at, but I'll explain that in a second.
If you want to use the cable card since like I said Verizon is very permissive you can use a few different software packages - Windows Media Center, XBMC, J River, Media Portal are the ones that come to mind immediately. Likewise you can use any of those with an antenna.
All the streaming services you listed can be used on a computer, but for most of them you have to leave the media center interface to use them, or at the very least need a mouse/trackball/trackpad type remote to navigate them. I believe XBMC has done the most work getting these integrated but I dont use it. I use WMC and have Pandora, HBO Go, ESPN 3, and Xfinity on Demand running inside of it, but I need to use a remote that had mouse functions to navigate. If you want a traditional remote centric experience you will probably want to use a Roku or similar box for streaming media.
As for the different locations here are your options:
-use Windows Media Center. use one main pc and several official WMC extenders
-use any of the software packages and stick a pc at each tv.
pros of using extenders: recordings made on the main pc can be played anywhere. given that you have Verizon this is a non issue, but they could change their policy or you could be forced to switch providers. extenders are cheaper than pcs. they "share" a recording schedule meaning if you schedule the system to record CSI from your bedroom that scheduled recording will show up on all systems.
cons of extenders: they have lousy file compatibility. this is a non issue if you dont plan on ripping movies, but if you should decide to there are no extenders than can play back all common file formats. the Xbox 360 supports some streaming services, but you have to leave the DVR interface and also pay a monthly subscription to use them. The Ceton Echo doesnt support these (yet, I believe it is in development) and the discontinued extenders (which work very well for live tv) don't do streaming well if at all.
pros of multiple computers: more configurable. you can play all your media files. you can also do all the pc streaming services.
cons: you don't share recording schedules (at least in Windows Media Center. I think some of the other software packages can do this) meaning that each computer won't know that CSI is scheduled. this also will keep the recording from being centralized - each PC will store their own recordings. you can network them and access everything though.
as far as emulators, thats a definite possibility. I know it can be done with XBMC, and this is how my WMC set up looks with my emulators. when a game is selected it launches the emulator in full screen to play the game. i set two buttons on my controller to map to ALT and F4, which I press together to exit the emulator and go back into the game browser: