What is the most logical next event?

How to start an online book group
Don't try to reinvent the wheel.
Before you even think about the first book you want to offer for discussion, take some time to peruse existing online book clubs and check out what kind of software they are using. You don't have to be a software engineer in order to create a website.
Think about how you would like the discussions to flow. You might want to use a message board system, an email system or a blog.