How do you data mine your web analytics?

For a new web site and subscription service, we would like to collect detailed metrics about how customers/prospects are behaving. We think our main interests will be:

(a) how people are finding us and how effectively we convert visitors to our site into paying subscribers;

(b) the usability of each feature of our service;

(c) patterns in how users access the underlying data and in which of our features they use to work with which kinds of data.

Our goals are to make informed choices about how to develop the data and features on the service, and to optimise prospect conversion and customer retention on genuine merit. That probably includes things like knowing the demographics and regions where we're succeeding or failing, but we're not interested in selling users' personal data to advertisers or anything similarly dubious.

I'm sure many here have been in this position, so please share what you've learned about different types of testing, which tools you find useful, which analyses you perform on your logs, and perhaps most important, how you reached this point and how you improve your data mining techniques over time. Thanks!