Well I never competed in the Putnam and only took a couple of graduate courses (one in Economics and one in Statistics) as an undergraduate. I did have a very strong GPA and strong letters of recommendation. I went to a solid undergraduate state school (not ivy league or anything) and I managed to get fully funded offers to 2 "top 10" PhD programs for Statistics. So you don't have to be a crazy math genius to get in. This might not be the case for a pure math PhD at a top school but I can't really speak to that.
As a Freshman you have plenty of time. My Freshman year I didn't take any math courses at all (I thought I was going to study linguistics).
The courses that were the biggest indicators of aptitude in Statistics at a graduate level I think were: 1) a proof based course on Real analysis and 2) an upper undergrad/grad course on mathematical statistics (covering things through Cramer-Rao bounds, Maximum likelhiood estimators etc). If you feel comfortable in those courses then I think you'll be fine. As a general rule, the more math you take the easier time you'll have. It's easy to pick up the statistics, it's harder to pick up the math. Although taking courses on Abstract Algebra and Topology while helping you with mathematics, probably won't be very useful as a Stats PhD. Focus on Real Analysis, Calculus, and Linear Algebra.
As far as interest, I mean if you're already looking at things like the Netflix competition and think that's cool, that probably says enough (Machine learning is also my area of interest). Read some papers in the area (don't expect to get the math but the intro and conclusions usually gives you a general idea of what they are trying to do). Other than that take some statistics classes and if you find yourself thinking and talking about statistics even when you don't have to I think that's a great indicator.
Feel free to PM me if you have any specific questions that I might be able to help with.