Will using an HDMI cable for an external monitor produce better graphics than using the VGA cable?

HDMI and VGA are both video interfaces capable of carrying computer display data to a monitor. HDMI is digital, VGA is analog.

HDMI is NOT inherently better than VGA. Each will support a wide range of screen resolutions and it is the screen resolution and color depth that affect the image quality rather than the interface used. Choose a graphics card that supports the resolution you need and make sure it has the output you need to connect to your monitor.