Before we jump into specific machine learning technique, I want to come back to feature extraction. A machine learning analysis will be only as good as the features that you plug into it. The best features are the ones that carefully reflect the thing you are studying, so you're likely going to have to bring a lot of domain expertise to your problems. However, I can give some of the “usual suspects”: classical ways to extract features from data that apply in a wide range of contexts and are at the very least worth taking a look at. This interlude will go over several of them and lead to some discussion about applying them in real contexts.
Here are several types of feature extraction that are real classics, along with some of the real-world considerations of using them: