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.

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'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.