Steam Link ($50) is a remote "workstation" device that allows you to play Steam games from the connected PC to your TV. Both the Steam Link & the desired PC MUST be on the same LAN to work. This will also tie up the PC you're connecting to (so your brother cannot be using the computer at the same time you're using it through the Steam Link).
As for connections, it's HIGHLY RECOMMENDED that you have a wired connection (between the Steam Link, router & the desired PC), but a modern WiFi connection (802.11ac highly recommended or 802.11n w/ 5.0 Ghz band. 802.11g is the bare minimum) can be utilized. Since the remote PC has to pump out video to the Steam Link & take the input from Steam Link, you will need a fair amount of network bandwidth for it (around 20 - 40 MBps). If your WiFi connection isn't that great in your basement OR in your brother's room, you may want to consider purchasing a powerline adapter to help improve the connection (WiFi extenders / repeaters are OK, but they can reduce your network speeds in half).
For the initial set-up, you will need to log into the PC you want to connect w/ the Steam Link as you have to enter a "Pairing Code" so the Steam Link knows what PC that it's authorized to connect to. This is probably the only annoying thing as you have to physically access the desired PC.
In terms of internet usage, the Steam Link utilizes minimal data as everything is being done within your own LAN & doesn't touch your internet connection / modem. The only time the Steam Link will use online data is for firmware updates. If you play any games online via the Steam Link (like GTA Online, Team Fortress 2, ect.) the data usage will run through the remote PC instead of the Steam Link itself.
Hope this helps!