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...