Approaching data science
The Udacity Data Analyst Nanodegree gives a very gentle introduction using Python and R for mostly exploratory Data Analysis which I think is what you are looking for. (It's not tailored towards business analysis. The courses are free and you can just take the ones you think are interesting. In your case, I would skip the ones about data visualization with javascript and data wrangling with MongoDB.) THey provide a bunch of resources to go from there. Of course there are plenty of other online courses. 

If you are more into books you could check out Tukey's Exploratory Data Analysis. A classic that is still highly relevant.

In terms of tools, the most commonly used are R and Python and I would focus on them for now.