To get 144 Hz, it is ideal to use a DisplayPort. This is because it is more capable than HDMI.
The DP 1.0 or 1.1a can produce an output 144Hz at 1080p. The 1.2 or 1.2a versions can do the same at 1440p, the 1.3 version at 120 Hz and the 1.4 version at 4K resolution, all using the DSC or Display Stream Compression technology.