Alternative to Alienware Alpha

[times_champion]

I currently do most of my gaming on a PS4, and I have a desktop PC upstairs which is about 3 years old now. I am thinking about getting a new PC for work stuff and some light gaming on strategy games etc so I was thinking about a laptop. After looking around though, it seems that I could sell my PS4 and get a £580 I5 Alienware Alpha which would outperform the PS4 as well asplaying emulators on my TV and being able to be portable enough to take upstairs and use with a monitor for word processing etc.

I have also seen people online saying the Alpha is a rip-off however and it's better to build an alternative. I'm not that concerned about having something he same size as the Alpha, but any PC I buy would have to have the following:

Small enough and portable enough to fit under to and take into a different room with minimum effort (max twice the size of Xbox one?
Powerful enough to play multiformat games at better settings than PS4
8gb ram + 1tb HDD
Under £550 without monitor but including Windows

If I can't find any decent alternatives for desktop or laptop then I'll happily buy an Alpha, but I thought I would check out the alternatives first.

 

[times_champion]

Thanks, would this spec outperform the Alpha/PS4? Is it pretty small? Also I'm not sure about B grade parts, is there any alternative?

 

[times_champion]

Thanks guys. Yeah, the Alpha GPU is based on the 860m apparently. The only issue is that the case looks pretty big. I will have to look at the dimensions, but it seems more like a smaller tower than a console size? Is there any way of getting all this into a smaller case, as I say around double the size of the Xbox One ideally?