Use either displayport or DVI Dual Link.
The problem with VG248QE is that sometimes its displayport acts strange for some reason. In my case it caused the motherboard to go nuts and prevent booting up because of excessive voltage on USB ports (don't ask me, no idea what was that crap about, but switching to DVI solved the issue).
The DVI is another story, you specifically need the Dual Link variant, but you can't use cables much longer than 2~3m. The cable supplied with the monitor will output 144hz.
HDMI 1.4 ports could technically push 120Hz (they can push 30Hz at 4K), while HDMI 2.0 is intended to push 60Hz on 4K, which should give it enough bandwidth to output 144hz 1080p.
But, you shouldn't be using HDMI for high refresh rate monitors anyway, displayport is the only modern solution, with the DVI-DL being the fallback option.