Really good question! There are a lot of ways to go about it. I would recommend trying to get a broad overview of the subject so you can understand the different models suitable to different situations and have confidence in learning new things. Machine learning is probably the best place to start since you will be expected to have some familiarity with it if you do AI. I would recommend learning about, in this order: linear regression, ridge regression, cross validation, decision trees, k-means, basic neural networks, dimension reduction, bandit algorithms, and hidden Markov networks. That way you have tools for regression to find equations to fit data, cross validation to tune parameters that cannot be learned by the model you're working with, decision trees for combining weaker classifiers to create stronger classifiers, k-means to find clusters in your data, neural networks to learn without having to specify your parameters (just hyper-parameters which can be tuned by cross validation), dimension reduction to remove irrelevant parts of your input data to speed up learning, bandit algorithms to learn while a system is being used (balance using what you know with exploring to learn more), and hidden Markov models to model the influence of hypothetical variables in sequence data.

My own biased opinion is to learn modal logic and also implement a propositional theorem prover in Prolog.