IMO they will all be more than sufficient for what a med student researcher needs to do, so it's probably best to just work with the one you prefer.
The place I think SAS really shines over Stata is cleaning and manipulating data. You can have numerous large datasets loaded at once and it's very easy to play around with them until you build the set of variables you want. For something like Medicare data where you have numerous different files containing various pieces of data for the same patients or physicians it makes it pretty simple to merge them together. In Stata you get to have one open at a time. The SAS language and formatting are kind of picky, but not that hard once you get the hang of it. The other thing SAS has going for it is that the previous generation of epi/biostats people were all trained to work with it , so it makes it a little easier to communicate with them if you understand SAS commands and output.
Stata is a little more user friendly IMO. The interface is easy to navigate and the language is more straightforward (at least to me). It also does some things very easily that I think are a pain in the ass in SAS (collapsing across observations, destringing variables). Neither SAS nor Stata makes beautiful base graphics but they can fine with some work (Stata imo is better in this regard).
I've used R much less than the other two, so I can't comment much on pros and cons. New statistical methods show up in R before the others since users can write their own programs. It also makes nice figures, and as mentioned before, it's becoming much more common to learn so in the future it may be beneficial to know it in the way SAS is now. I believe most of the bioinformatics people use R exclusively now (via bioconductor project).
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