First of all, welcome aboard
Any experience building custom PC's? If yes, then I suggest doing so!
As for your specs, I recommend Windows 7 instead of 8 as it has better compatibility for games, and to make sure what video card it is, not just the video memory; e.g. 1GB. If it is Geforce, I recommend not less than GTX 650 Ti. Some stores just advertise the video memory as it if is the thing, but the chipset is what really matters the most!
That was for the technical part. As for the price part, all I can say is desktops are typically cheaper than laptops of the similar specs!
Best of luck with your search!