For a broad(er) perspective on AI, checkout UC Berkeley's CS188 http://inst.eecs.berkeley.edu/~cs188. I think it's a good entry course into AI. One advantage is that the math requirement is not as high as Stanford's CS229 or EE263 (both of which are fantastic courses to be clear, but are easier to appreciate with the correct background).
I know Machine Learning is a subset of AI, but lately I'm beginning to see it more of under Statistics. That's just my impression, I could really be wrong given my very limited knowledge.
Yep your intuition is good -- a lot of the mathematical techniques used in Machine Learning are motivated/derived/understood from Statistics. I'd recommend starting with a broader approach to this topic. In particular, there are often simpler heuristic approaches to a problem that are reasonably good and worth trying before trying to build a full-blown ML system. What I've learned is that knowing where ML systems fail/are overkill is just as important as knowing when to use them/build them.
If you have already brushed up on linear algebra and calculus (which you're gonna need if you want to do any serious ML) take a look at Hastie et al's Elements of Statistical Learning.
The PDF is free, and the book is both extremely well written and super comprehensive.
http://www-stat.stanford.edu/~tibs/ElemStatLearn/
You might also want to check out R, as its an amazing statistics language which has hundreds of packages available for ML. There's a large user community, and the really obscure error messages you get will teach you a lot about statistics. http://cran.r-project.org/
Also, a lot of machine learning is getting the data into a usable form, so learn how to use Unix command line tools such as sed, awk, grep et al. They are absolute lifesavers.
