As Fast As Possible
To output 1080p content at 144Hz, you will need either a dual-link DVI, a DisplayPort, or an HDMI 1.3 or higher cable. For 144Hz at 1440p, you will need at least an HDMI 2.0 or a DisplayPort 1.2 while for 4K 144Hz you are going to need an HDMI 2.1 or alternatively, the DisplayPort 1.4 which maxes out at 120Hz without compression.
VGA & DVI
VGA (Video Graphics Array) or D-Sub is an old analog connector which maxes out at 1920×1200 and 75Hz. Most of the newer graphics cards and displays don’t feature this port. It can still be found on some monitors though which can be useful if you want to connect it to an older GPU or use it for a multi-monitor setup.
DVI (Digital Visual Interface) is a more common and widespread connector, but keep in mind that not all DVI versions are the same. Only the Dual-Link DVI can do 1920×1080 at 144Hz or 2560×1440 at 75Hz while the older DVI ports max out at the same bandwidth as the VGA.
Nowadays, most of the monitors, TVs, and graphics cards feature at least an HDMI 1.4 which is enough for 144Hz at 1080p, 75Hz at 1440p, and 30Hz at 4K.
The next version, which is the HDMI 2.0, is also fairly standard and can be used for 240Hz at 1080p, 144Hz at 1440p, and 60Hz at 4K. The latest HDMI 2.1 adds native support for up to 144Hz at 4K and 30Hz at 8K.
Apart from an HDMI, most of the gaming monitors also come with a DisplayPort 1.2 which offers native support for 240Hz at 1080p, up to 165Hz at 1440p, and up to 75Hz at 4K.
The DisplayPort 1.3 and 1.4 provide the extra bandwidth required for 240Hz at 1440p, 120Hz at 4K, 60Hz at 5K, and 30Hz at 8K. The main difference between the DP 1.3 and DP 1.4, is that the latter supports DSC (Display Stream Compression) which allows it to deliver 144Hz at 4K, 120Hz at 5K, and 60Hz at 8K – but with compression.
A mini-DisplayPort (or Thunderbolt) connector can output the same amount of bandwidth as the DisplayPort implementation it is based on. So, a mini-DisplayPort 1.2 can do 75Hz at 4K, 240Hz at 1080p, and so on.
Furthermore, the mini-DisplayPort is being replaced by the USB Type-C port on the newer displays. The USB-C sends the DisplayPort signal for audio and video and can simultaneously charge and transfer data to the connected device such as a compatible laptop, smartphone, etc.