Uhmm really this is gonna cost you some serious bucks, there is no 'cheapest way' unless you want to do it instead on a PS3/Xbox 360. There is cheap ways to filter off the video for 'streaming' play for consoles without affecting FPS, but for PCs it is totally different and going to either cost you cash or FPS. The standard is: Whatever FPS you normally get in your game CUT IT IN HALF when your videoing (streaming LIVE is even worse!) the gameplay. This is because the demands are very heavy for creating video content, and 'live' feeds are even more demanding, then oh yeah you want excellent gameplay, well my dear this is EXTREMELY demanding.
Lastly, if your on 'generic' consumer cable internet, your 'upload' speed (what your stream relies on) can be 1/10th your 'download' speed. So if your on the 50Mbps cable package, your MAX upload speed is 5Mbps. Another cost you will have to endure, if you want to 'stream live' like the 'good feeds' which usually are on FIOS (Verizon) which as the same Up as DOWN speeds. Cabel by the way will tell you they can up your speed, but more then likely they will suggest you need to switch to BUSINESS CLASS Internet (very costly) to be 'allowed' that much bandwidth 'server' style (your serving your video out to people to see as much as Game.TV website serves its website for you to visit).