I would recommend the ACR122U. Everybody has one: it’s the go-to reader for HF implants when you don’t know what to get and you’re not sure what to do with it. It’s supported by just about everything under the sun.
As for logging in using that reader - as well as many other types of readers - under Linux, weeeell… you’re in luck: I have just the thing for you 
Be aware that it requires some manual configuration, and it requires you to know your way around a Linux system, because I couldn’t be assed to write an installer. But there is a well-documented README.