Home Game Streaming Devices

Hi Community

I wanted to ask everyone's opinion on what device I should get so to stream a game from my bedroom upstairs to the big HD TV downstairs in the back room.

My computer specs:
-i5 4460 3.20GHz
-MSI GTX 970 4GB
-Corsair Vengeance DDR3 1600Mhz 2x4GB Dual Channel 8GB kit
-1920x1080 LG monitor
-500w Corsair CX Bronze
-1TB WCD Hard drive
-ASRock Z97 Anniversary Motherboard
-Windows 7 Ultimate

To access the internet my PC is connected via LAN to a WIFI booster that is plugged into the wall in my room, the WIFI booster connects via wireless to another one plugged in a wall in the back room which is then connected via LAN to the Virgin WIFI Super HUB. As my room is a WIFI dead spot speed wise for some reason.

With the WIFI booster I have download speeds of 4mb/s on Steam at the most, we have 60meg internet but most of that is used by the Virgin TV box and the rest of the household.

I have heard of Nvidia's streaming device but that has a subscription right? Is Steam's streaming box any good?
 
the Steam box is for LAN use, and has no subscriptions I know of. Also, Steam streaming in house uses LAN. Any spare computer will do for in house, and it'll use the LAN. The only internet access will be what's needed for the game itself.

EDIT - Wireless LAN is still faster than wireless internet access. But you're always best wired.
 
How does the Steam Link work with a computer? Does it just connect to a pc then uses the Steam OS big picture mode where the person justs pick a game that is installed on their Steam that has controller use?

Does a controller come with it and how does the controller work with the Steam Link while the Steam Link is connected to your over your home internet?