Check that out, and see what other questions you have. They key is not to start by asking what kinds of tests there are or what kinds of test can be run, but rather first asking "What are my requirements" and then developing the proper tests to validate those requirements.
Unfortunately, the three articles I have written about types of test and their value are currently in edit and have not been promoted to the site yet.
I'm glad you found it useful. That is years of consulting lessons roled into a single doc. It looks kinda simply now, but let me tell you, it was a log process to learn what questions to ask the client when they THOUGHT they already knew what (and how) they wanted tested.