What is the proper way of importing rigs from one blend file to another? I bought a blend file which contains 3 rigs and I need to import one of them into my other blend file for animation. I know you can Link blend files together and I was wonder what do I need to link? I see tons of options and from different folders as well. What do I need to import and from where so I don't break the rigged model?

Example of things I can that I can link: 



I know this also depends on the blend file as well so whats the easiest way to do this?
You'd better select in the source file all elements you need, Ctrl G create a group, rename it and then save, close, open the new file and APPEND that group. If you use Link instead of append, your rig will not be directly editable in your new file, you will have to make the edits in the source file.
To avoid confusion create a group even with a single element (the rig you need), then you can delete it in the new file: everything will automatically imported correctly.
Anyway, if you need only one rig (one armature with all related bones and constraints) you can rename it and simply append that armature.