Never a laptop for gaming unless you REALLY need it.
If you were to build a gaming PC within a budget then I would recomend the following:
http://www.pccomponentes.com/core/client/showList/id/384694/hash/GVMteDys
you COULD get a better CPU but if your not going to OC and you just want a pc to game on in 1080 then this is more than enough.
I have also chosen a mini itx board that has both wifi and that you can overclock with IF you would want to upgrade the CPU down the line.
The case and MINI ITX is for the looks and if you have to move around then you can easily take it with you.
You could go i5 and skipp the ssd, but with this GPU its a perfect match. Price - Performance and looks - its a great small pc.