Here's what I'd recommend.

GETTING STARTED WITH DATA SCIENCE

If you're interested in learning data science I'd suggest the following:
 

Tools

1. I’d recommend learning R before Python (although Python is an exceptional tool). Here are a few reasons.
   
   1. Many of the hot tech companies in SF, the Valley, and NYC like Google, Apple, FB, LinkedIn, and Twitter are using R for much of their data science (not all of it, but a lot).
      
   2. R is the most common programming language among data scientists. O’Reilly Media just released their 2014 Data Science Salary Survey. I’ll caveat though, that Python came in at a close second. Which leads me to the third reason:
      
   3. R has 2 packages that dramatically streamline the DS workflow:
      
      • dplyr for data manipulation
        
      • ggplot2 for data visualization
        
        Learning these has several benefits: they streamline your workflow. They speed up your learning process, since they are very easy to use. And perhaps most importantly, they really teach you how to think about analyzing data. GGplot2 has a deep underlying structure to the syntax, based on the Grammar of Graphics theoretical framework. I won’t go into that too much, but suffice it to say, when you learn the ggplot2 syntax, you’re actually learning how to think about data visualization in a very deep way. You’ll eventually understand how to create complex visualizations without much effort.
         
        
        Skill Areas
        My recommendations are:
        
        
2. Learn basic data visualizations first. Start with the essential plots:
   
   • the scatter plot
     
   • the bar chart
     
   • the line chart
     (But, again I recommend learning these in R’s ggplot2.) The reason I recommend these is
     
     1. The are, hands down, the most common plots. For entry level jobs, you’ll use these every day.
        
     2. They are “foundational” in the sense that when you learn about the underlying structure of these plots, it begins to open up the world of complex data visualizations.
        As with any discipline, you need to learn the foundations first; this will dramatically speed your progress in the intermediate to advanced stages.
        
     3. You’ll need these plots as “data exploration” tools. Whether you’re finding insights for your business partners or investigating the results of a sophisticated ML algorithm, you’ll likely be exploring your data visually.
        
     4. These plots are your best “data communication” tools. As noted elsewhere in this thread, C-level execs need you to translate your data-driven insights into simple language that can be understood in a 1-hour meeting. Communicating visually with the basic plots will be your best method for communicating to a non-technical audience. Communicating to non-technical audiences is a critical (and rare) auxiliary skill, so if you can learn to do this you will be very highly valued by management.
        I usually suggest learning these with dummy data (for simplicity) but if you have a simple .csv file, that should work to.
        
3. Learn data management second (AKA, data wrangling, data munging)
   After you learn data visualization, I suggest that you “back into” data management. For this, you should find a dataset and learn to reshape it.
   The core data management skills:
   
   • subsetting (filtering out rows)
     
   • selecting columns
     
   • sorting
     
   • adding variables
     
   • aggregating
     
   • joining
     You can start learning these here. Again, I recommend learning these in R’s dplyr because dplyr makes these tasks very straight forward. It also teaches you how to think about data wrangling in terms of workflow: the “chaining operator” in dplyr helps you wire these commands together in a way that really matches the analytics workflow. dplyr makes it seamless.
     
4. Learn machine learning last.
   ML is sort of like the “data science 301” course vs. the 102 and 103 levels of the data-vis and data manipulation stuff I outlined above.
   Here, I’ll just give book recos:
   
   • An Introduction to Statistical Learning.
     This is a highly regarded introduction
     
   • Machine Learning with R
     
   • I’ve also heard that there is some foundational ML information in R in Action, though I haven’t read it myself.
     
     After you get these foundations, then you can move on to specialize in a particular area.
      
     

     OTHER RESOURCES:
     

     Data Visualization
     

5. Nathan Yao of Flowing Data is great. His blog shows excellent data visualization examples. Also, I highly recommend his books. In particular, Data Points. Data Points will help you learn how to think about visualization.
   
6. The book ggplot2 by Hadley Wickham. This is a great resource (though a little outdated, as Hadley has updated the ggplot package).
   
7. I also really like Randal Olson’s work (AKA, /u/rhiever). He creates some great data visualizations that can serve as inspiration as you start learning.
    
   

   TL;DR
   

   I'd recommend learning R for data science before Python. Learn data visualization first (with R's ggplot2), using simple data or dummy data. Then find a more complicated dataset. Learn data manipulation second (with R's dplyr), and practice data manipulation on your more complex data. Learn machine learning last.

Yep, humans perceive differences in length much better than differences in angle. Yau's book Data Points talks about this extensively with examples.