How can I rank my games by number of achievements remaining?

You can try using AStats, it generates a list of games with achievements for your Steam account that you can sort by multiple criteria such as "number of achievements remaining" as you mention, and also by "hours to 100%" (based on how long it took other members to complete the game), and others.

It's a pretty handy website for Steam game completionists.

I made a thing that does this. Enter your vanity URL and sort by percent.