the USB port on the FireTV Stick isn't a USB-OTG (you can't plug in peripherals to it) I read so you may be limited to Bluetooth only... which may be wonky at best :/
I sure hope we get an update to the Android app or at least a Chromecast app or something
EDIT:
The Razer Turret seems like a good KB/M option for Comfy Couch
Can the Raspberry Pi do 1080p60 with no issue on Limelight?
may look into getting one - hope the DS4 works well with it
Yes RPi has no issue 1080p60 over LAN atleast.
You will need to check forums for controller support.
My 360 pad stays connected to my host PC when I used limelight pi in another room. I know the USB ports on the Rpi don't have enough power to run the 360 wireless receiver.