I have a PhD in statistics from the University of Minnesota, and I also have read extensively on machine learning since the degree and have used that learning on the job. Statistics programs vary widely in their emphasis, so the answer to your question comes down to exactly what direction you want to go into. Loosely speaking, the main statistics directions I see (in the health area) are clinical statistics, industrial statistics (including optimal experimental design), and machine learning. There are some who do two or more of these well, but most statisticians do well at one. A machine-learning expert is not necessarily an excellent applied statistician, and vice versa. You need to think about what exactly you want to do and then find a department (statistics or c.s.) that best achieves it. One thing to ask yourself: do you want to fit models and analyze data after it's collected, or do you want to be an interactive contributor to the design of the data collection and the evolution of a project? The former is more in line with machine learning, the latter with applied statistics (traditionally understood). They require different skills. Nothing says you can't do both, but most statisticians and machine-learning people I know don't. General advice: pick a program that will cover decision theory. This provides a valuable perspective that is often missing. It's possible to have an interesting type of model but miss out on how best to evaluate it or make predictions with it. At that point you're in the world of clever ad-hockery. Also, check out Hastie and Tibshirani's _The Elements of Statistical Learning_.

Check out _Mathematical Circles_ by Fomin, Genkin, and Itenberg, 1996, now published by the American Mathematical Society. The book is composed of problems for math clubs and teams. The problems are very engaging and creative. ("Cut a whole in an ordinary piece of paper such that an elephant could walk through it.") The chapters are organized by theme, and they build conceptually within chapter. I've been going through this with my 11-year-old homeschooling daughter, and she loves it, and has come to love math. Have a student read just one chapter at a time (the whole book would be too ambitious). Your students will discover the fun and creativity of math!