Which machine learning concepts do I need to know for this data mining problem?

I'm hoping someone can help refresh my memory about which concepts I'd need to know to start new data mining project. I'm hoping to keep this limited to concepts since I already have a structured dataset and software platform (I can figure out the rest).

I've already built a reliable system that stores a structured dataset for event, conversion, and identity data. I need to mine this data and segment it according to which events lead to conversion, etc. Each event has properties that I'm including in the analysis. Most importantly, the number of "segments" derived from this data need to be adjustable. The user can produce 5 or 10 "optimized" segments according to his/her input.

I'm wondering which machine learning patterns might be most helpful here? And what mathematical concepts I will need to brush up? I don't often work with machine learning so thanks for your help!

Edit: I'll add that I'm currently looking at using k-means clustering to achieve this problem. Might be helpful if someone can validate that approach.