You may want to look into getting a gaming laptop instead of buying a pc and a laptop.
-asus rog, msi, clevo, gigabyte,...
-benefit is its alot more portable and all your stuff is in one place(a gtx 860m should be able to max most games)
The two laptop branches i can currently recommend purely for work(little light gaming-none): any mac(pro, air), or a surface pro
-both of these have proven quite reliable among my schools population with quite large battery life (i can give a run down on the benefits of either if you wish) (i can also talk about other laptops)
Honestly, that i7 3770 is good enough that people(including me) would buy it easily, haswell's main increase over ivy bridge is energy efficiency(less heat) not performance(however the 3770 is non-k so you cant overclock it). It may be reasonable to use that processor you have on hand(and spend more money towards the laptop).