Computer that can run LoL on high settings

maybe? it shared video memory which means that its uses system resources to run the graphics.

You really need to find exactly what gfx you are getting with it. Maybe ask them to load a game on a display model so you can see how well it preforms(if you are going to a store)

I have something like this http://pcpartpicker.com/user/QuantumTime/saved/PJkWGX

Doesn't anything work? My old laptop works on high settings no problem. So I wouldn't be too worried about that.