Option 1 - Create a high res and low res image for screen.
The image below is 2000px by 2000px
The next image is 300px by 300px
Option 2 - Create a high res and low res image for print and print them out.
The photo below is 500px by 500px at 300dpi (High res! Although my printer is rubbish!) I printed it out and then took a photo of it.
This next one is 500px by 500px at 72dpi.
You can see the first one is much better! <3