Having seen a tiny part of the baseball statistician world myself, I can offer a few points that may help. First, read all of the advanced baseball sites you can - Fangraphs, Baseball Prospectus, Beyond the Boxscore, etc. The articles will help you understand what tools are used for analytics and what questions are being asked. R and SQL are commonly used for statistical analysis and database management.
OOTP does have some stats export stuff that you can use to sharpen up on your analysis but there are also plenty of real-life baseball stats that you can download and play with as well. One thing that may help you get started is to download the Baseball Databank (
http://www.baseball-databank.org/) and then calculate wOBA (
http://basql.wikidot.com/woba).
You can also follow a bunch of the baseball database experts on Twitter and may even find some of those currently working for real MLB teams. They're pretty active there (or at least were a few years ago).
Mike Fast, Colin Wyers, Daren Willman, Christopher Long, Tom Tango, Alan Nathan, etc. are all people that helped me or have incredible resources online.