What's the most versatile and well supported back-end language? Is using one and a different one for front end better than say using JS for full stack?
There are no best language. It would be more about you need, that will result in the best language for your need.
But if you really need a answer, C#, NodeJS, Python are all really nice. Actually there are probably the most common in the industry for back-end.
Please note too, when you work for someone, you don't always choose you language, you usually just deal with it.
Indeed there is no best answer, considering the fact that the choice depends mainly on your application and needs. The thing is you can even write your back-end in C++ with say the Qt framework for instance. You would have total control over how your back-end reacts to the client side and you can make your code really efficient. But do you really want to reinvent the wheel ?
The question you should ask would be: will the back-end coded in my favorite (where you feel most at ease) language fulfill my (client's) need ?