I recommend Chadwick's little book The Decipherment of Linear B. It's readily available, and he vividly describes his work with Ventris and how they justified their conclusions. I don't think there's been any big news in the field since their decipherment.

The Mycenaean texts largely confirmed pre-existing reconstructions of proto-Greek. There were some interesting points, which probably indicated that Mycenaean wasn't quite the direct ancestor of the later language. Also, because of the cumbersome and un-Greek nature of the writing system, a lot of detail can't be recovered. But basically, if a new text in Linear B were to be discovered, there would be little difficulty in reading it.

As to what it says about the culture of the area, I'm not the person for that.