In reply to mostly harmless:
Like you, I have a physical science background, and decided that I finally ought to get to grips with this thing called stats that my biology/social science/psychology colleagues talk about but seem very afraid of.
Have you thought of doing a MOOC?
I have done several now in the stats/data science field, and find them very helpful as a way of giving focus and discipline to my learning. The emphasis ranges from classical stats to the wider field of statistical learning, data mining ,data science, analytics - whatever you want to call it.
They are all free, including the assessment, or you can pay £30-£50 per course for a verified certificate, if you want one.
There is a whole series of nine courses from Johns Hopkins University called Data Science, on the Coursera platform. I have done the first seven of them, and start the last two in a few days. They are dense, fast-paced and will give a lot to do if you take them two or three at a time as I have done. Only two, Statistical Inference and Regression Modelling focus on what you possibly mean by stats, but the others give you really good (I think) practice in actually solving and presenting problems - so you learn how to use R, Git and GitHub, how to get and clean messy data, how to do exploratory analysis and how to use the various graphics packages in R.
Many find the approach overly mathematical, but you might like that. I do.
Another one I am part way through is The Analytics Edge, offered by MIT on the EdX platform. This also gives a lot practice in R, with a very wide range of examples of the use analytics, for example in the stock market, in health, in sport. The assessments are time consuming but straightforward, or at least they were until the current one, which is a Kaggle Competition.
In September (good timing for you) I am going to start another one, which is highly rated, called Data Analysis and Statistical Inference, from Duke University on the Coursera Platform. It also uses R and has a free text book online that they will use. (All the JHU materials are on Github/Youtube too).
I could in principle do all this myself just by looking at websites, but the courses move you along and make you do assessments, in which most of the effective learning takes place.