I'm building an app that will store some of our clients details, things like usernames / passwords, information that we need to remember and keep secure.
What's the best method for storing this information securely?
Such an open-ended question with not a lot of detail to go on. I'd suggest reading Chris Shiflett's excellent "Essential PHP Security" before you go any further. It's short, to the point and very practical.
There's also a reasonable amount of the advice available from the book's website too at http://phpsecurity.org/