What data analysis software should a supervisor recommend to their research students?
Teaching how to program should be a priority in research, in at least Sciences. Doesn't matter what STEM field you are in, almost certainly you will need to deal with data, and using "black box" software only teaches to do whatever the software tells you. 

I've seen people give results using standard deviation and mean for non-normal distributions, and its just because they didn't know how to plot their distribution and just used black box software. I've seen people rename file by file a folder with 500 files with data. These are worse than "Attack ships on fire off the shoulder of Orion".

Since nowadays almost all research in STEM is performed using computers, understanding computers is a must. 

My recommendation is to make people learn MATLAB if you have access to it, or Python if you don't have access to MATLAB or you are a Open source / free software supporter. Both of this languages are designed to be very high level, and not need "advanced" computer science skills (such as inheritance in OOP, or pointers in C)*. Both of the languages are widely used and there are numerous free online courses to learn, in Coursera, Codeacademy, Udacity, EDx or any other online learning platform.

Learning how to code to the basic point should take less than 2 months, considering that meanwhile the student is also doing other things. And they can save thousands of hours of tedious work.

Let me repeat the key message: We need researchers with programming skills. Its incredibly important skill to be able to perform research in the XXI century. 

While this answer mainly focuses in STEM, basic programming in other fields that use statistics is also useful. 

*Of course, knowing about that helps.