Background: I am a masters student in stochastic analysis. My course is very theoretical, which in general is fine by me, it is what I enjoy the most. From the more data-friendly subjects, I have (or will obtain/deepen) knowledge in stochastic processes of all kinds, time series, statistics, linear regression. Apart from those my course focuses on stochastic analysis, stochastic differential equations, spatial modelling and point processes.
Motivation: The final impetus that lead me to write this question is quite simple: recently I stumbled upon a data-analysis student competition in my city and thought about entering. I quickly realized I have literally zero idea what to do with data. Not that I am not good at it - I literally have no actual knowledge, apart from being able to answer narrow questions in statistics and regression from classes, possibly model the simples processes if I try very hard.
But more generally, I simply feel that since I am a mathematician, having data analysis skills is the sort of low-hanging fruit and it would be a great shame not to learn anything about it.
Goals: Here lies the problem. While I have a vague idea, my lack of knowledge is such that I do not know what is it I want. I understand this does not make for a well-posed question, but I am hoping shaping my goals is what Math.SE will help with, too. I think I'd like to stick with R, since it's a free software that I'll always be able to use (unlike Mathematica), but software choice is secondary. Vaguely, I'd like to:
1) Have the knowledge necessary to be able to theoretically compete in such a competition (doing badly is fine, but currently I am wondering about entering a marathon having only read about "legs" and "running" on wikipedia)
2) Be able to most utilise my knowledge of mathematics and make it my strength - if I competed against other people I'd probably be stomped into ground by even those who have just basic statistics and time series knowledge, but are good at working with data. Moreover, if I could somehow incorporate actual stochastics/spatial modelling, that would also be an interesting option.
3) I'll take a stab at guessing my goals - be able to do basic statistics/regression in R, model different processes, do experiments with random variables from different probability distributions, have the basic toolset for time series. Beyond that I'd really be completely guessing.
Questions: 1) What do I study? Are there topics/books considered to be the basics?
2) How can I best utilize my strengths - i.e. deeper understanding of mathematics? Say if I somehow had to compare data using an interesting metric that requires good deal of knowledge of metric spaces to be understood (yeah, I don't know what I am talking about). Then again, it's very likely that the simpler, the better. I'd simple like to be aware of possible strengths, but I really do want to be able to walk/crawl properly first.
3) The main question: what resources would you recommend for me, i.e. someone who isn't afraid of (or even welcomes) complicated mathematics? That is not to say a simple book may not be far more important, but I am not limited to them.
This is primarily a reference-request question (also to make it easier to answer, I suppose), but any answer consisting of general tips and thoughts on this matter will be very welcomed, too.
Btw, I wouldn't want to make it sound like a competition is the main motivation for me, as it really isn't. It's just that I think it's a useful benchmark for the "real-life" data skills I learned.
Thanks for any help!