Can only speak for Steam's streaming here, but your mileage will probably vary. Your system needs to be fairly beefy (you will get a bit of a performance hit from streaming games). I run a geforce 1060 and it'll stream any new games at 1080p / 60fps but I'd go beefier for 2K/4K streaming. I'm still on a dumb 1080p TV so that'll be more important if your TV is >1080p.
Biggest obstacle here was the wifi in this house is unreliable. We tried getting a wifi extender and even a new wireless router but we kept getting latency issues. We opted to get a powerline adapter for a stable connection. MOCA is also worth looking into if connectivity is a problem.
And finally, running to the other room to start games. Again, this is steam, but I'm guessing shield has the same limitation: if your system isn't logged in or the screen is locked, you will probably have problems starting games remotely in those cases. You'll want to setup remote desktop almost for sure (you can VNC or there's a way to logout of RDP too without locking the screen automatically). I also have a Wake on LAN shortcut setup to wake the PC up remotely.
Finally, sometimes games won't pipe audio remotely because they don't switch to the "virtual streaming audio device" these apps use properly. As far as I can tell this is on a game-by-game basis and depends how they coded it, but for that I have a pretty ridiculous work around (I remotely start a command line tool via openssh to force the audio device to "steam streaming speakers" then restart the game after that). The games with these problems seem pretty rare though, I'd say maybe 5% of the games I've tried.
Overall it's awesome and I glad I spent a day or two figuring it out. I don't get noticeable lag and I can stream pretty much any game to my living room on the TV now. Also got a "Couchmaster" for a kb/mouse setup. I can also emulate things like Wii U games and stream them remotely to the TV like having an actual system.
Hope this helps.