Would you say, "She was quiet after she'd been back from school," or "She was quiet after she'd gotten back from school"?

The simpler option is often the better option. Why complicate a sentence unnecessarily with the past perfect "after she'd been back"? Here is a simpler sentence:

After she returned from school, she was quiet.

If you were to add an extra time element to your sentence, however, it could be written using the past perfect, as in the following sentence:

After she had been back from school for three hours, she was quiet. [In other words, perhaps for three hours she was quite boisterous and outspoken, but when three hours had elapsed, she grew silent. The poor girl was probably talked out!]