How to set up a new widescreen LCD monitor with an old HP Pavilion XE783 desktop to get the correct aspect ratio that is to avoid horizontal stretching of the images?

Search for the monitor's model number on google and find out it's aspect ratio. Then write click on your desktop and go to Properties. Go to the Settings tab and adjust the screen resolution slider to any resolution where the ratio of the first number to the second is equal to your monitor's aspect ratio.

Or just try trial and error to find the best resolution.