As said above, the iGPU on the latest processors shouldn't be an issue at 1440p, it's the motherboard you need to look at most closely. You need to check that it supports 1440p
and that it supports it out of the same port you're going to use to connect to the monitor. For instance, some motherboards (
like this one) will only output 1440p over HDMI, not DVI, yet some monitors (
like this one) will only accept 1440p over DVI not HDMI. So check both before you buy.