MATLAB is amazing for general 'data science,' and is very widely used for certain tasks, such as image processing. It provides a huge array of already-implemented algorithms for computer vision, statistics, machine learning, and simulation. Many academic labs use it, and many students receive MATLAB training. On the other hand, MATLAB is proprietary and quite expensive. (It's semi-open source because most of it's functions are MATLAB scripts themselves). The language is very readable, except maybe the native array syntax, and comes with extremely good documentation, but it's clunky for general purpose programming. It has an OK IDE and one of the best debuggers in any language. The runtime is redistributable, so you *can* make portable applications, but again, it's a little clunky. The open-source GNU Octave and Scilab environments are also (mostly) code-compatible with MATLAB. All-in-all, it scores highly in all three aspects you mentioned, but it's very expensive.
Python is also very good, once numpy, scipy, matplotlib, pandas and ipython/jupyter packages are installed. Like MATLAB, Python is widely used in academia, and lots of students receive training. There are many function/algorithms already available, but somewhat less so than in MATLAB. For example, the statistics capabilities are similar, but MATLAB has more image processing functions. Plotting and visualization also haven't quite caught up to MATLAB yet. Python has the great advantage of being totally free and open-source, and there are a large number of IDEs and debuggers available. Python is also a great general purpose language for self-contained, portable applications that may grow out of data analysis code. The documentation can be lacking in some modules, but there's good free support online via e.g. stackoverflow. Python is readable and easy to learn. It scores about the same as MATLAB, weaker in some areas, stronger in others, and is completely free. There's active development of the analytics modules and going forward Python will probably become more popular for data science.
R is a bit of a special case. It has excellent statistics and machine learning capabilities, and there are a lot of extension packages available with specialized features, but it's really not as general as MATLAB or Python. I'm unaware of anyone using R for image processing, for example. As a language, it's very declarative, and the analyst doesn't need to understand statistics methods or their implementations in order to use them. That's great for beginners and convenient for experts, but can lead beginning/intermediate users astray if they don't appreciate the distinctions between significance and effect size, between different measures of significance/effect size, independence of variables, etc. Plots and visualizations in R tend to look nice when printed as PDF, but they're essentially non-interactive. R isn't general purpose at all, and personally I don't like its language conventions. I had the same experience with Mathematica, some people really like it and it's great for certain things, but I just can't stand the language. Back to R, I think the usefulness is great for statistics, less so for other tasks. Maintainability is OK - IMHO the language is not as intuitive as MATLAB or Python. My impression is that fewer people receive training with R, and it's a little less popular in general. It's the only one of these three languages I didn't see until grad school.
My first choice for any new data analysis task is Python. I think it has the brightest future, and it's available to everyone for free. I'll use MATLAB if one of its built-in functions will save me a ton of time, or if I need to prototype something very rapidly (I guess it's still my strongest language). R I only use if I absolutely need something from one of its third-party modules. Lately, I've been experimenting with Julia, but it's not close to mature enough for my academic projects, let alone commercial ones. Sometimes I use external visualization tools, like LLNL VisIt, if I need to make high-quality, interactive visualizations of very large data sets. Hope that helps, sorry for the wall of text.