NOT going to happen on that low, especially DayZ. Laptops cost 2x that of a comparable desktop, so while you can build a gamers medium class desktop for $700 (no you can't do less unless your going to go real lower graphics / fps) while any laptop the same is $1200-1400 or more. Add to that you want to 'record' which immediately cuts the FPS on any game 1/2 (anyone on Twitch.tv, etc. will tell you the same thing).
To do Dayz (se the ones on Twitch .TV yourself) that your broadcasting AND have at least over 30FPS, requires a i7 system, with a decent video card to handle both renderings (rendering gaming video, and rendering a video broadcast signal in REAL TIME). The other games you COULD bump down to a normal i5, but when recording, especially when alot of rockets are happening in TF2 or your trying to show your build in a panning out on the screen, will drop you into the teens to single digits for the same reasons.