This isn't going to be a tutorial, but some condensed tips.
The best way to get the avatar you want regardless of the size of the image is to link off site.
To make this work you need a direct link to the image. That means there's nothing on the page except the image. To do this, right click on your desired avatar and click "open image in new tab" (it might be different on Windows, but it will be something similar). *
Once you have that, put the link you get into the link off site thing. It should work. You will need to mess with the dimensions until they are within the limit and to your taste.
*Please note this will not work on Instagram images.