For statistical programming, since we're talking about R, I strongly recommend R for Data Science (http://r4ds.had.co.nz) by Hadley Wickham (who created a large amount of the R packages that are very commonly used [tidyverse] and incidentally also now works for RStudio)

A good book on statistical theory is harder to come by, though.

Introduction to Statistical Learning is free and quite good: http://www-bcf.usc.edu/~gareth/ISL/

Follow it up with Elements of Statistical Learning by three of the same authors for more advanced stuff.

I can thoroughly recommend Elements of Statistical Learning.

It won't teach you much about theoretical statistics, or even things like experiment design, but you will learn a LOT about regression, classification and model fitting which is what everyone seems to want to be able to do these days.

Perhaps not quite on topic, but introductions to statistics which take a Bayesian approach are starting to exist. Like http://xcelab.net/rm/statistical-rethinking/ or perhaps https://github.com/equinn1/MTH225_Spring2016 .

Each field has their own "good practical statistics book". I work in finance and so recommend Fabozzi. It's good, but so are many other foundational texts. Your requirement for practicality necessarily negates a one true answer.

I am currently going through this free book : https://www.openintro.org/stat/textbook.php?stat_book=os

It will depend a lot on your field, but a solid grasp of fundamental probability theory should be applicable everywhere.

I think this is an excellent overview [1]. Learning probability from a measure theory angle is more difficult to grok compared to the frequentist approach everyone is more familiar with, but I found it much more enjoyable. (I learnt the usual way from doing computer science undergrad, but now re-doing it more rigorously for masters in financial engineering)

[1]: http://www.math.uah.edu/stat/index.html

What can you do with the measure theoretic foundations vs the traditional approach? I know graduate classes typically take the measure theoretic approach, but it's never been explained to me why.

To be honest after one semester, I can't eloquently state it without rambling for a few hours, so I'll direct to this excellent HN comment, which does a much better job than I could:

https://news.ycombinator.com/item?id=14286604

What's your background and what exactly do you mean by modern methods? An Introduction to Statistical Learning is good and you can download the pdf: http://www-bcf.usc.edu/~gareth/ISL/ it assumes you have a pretty decent background in mathematics though.