A) Build on what you know. If you have done any programming before, Python is probably the way to go. Otherwise R is probably fine.
B) Learn enough of the other language to at least read it.
C) Always be learning and willing to learn.
In my (anecdotal) experience, Python data skills seem to be in great demand. I don't remember talking to anyone in my most recent job search that was looking for only R. Typically it was Python or Python and R. This may be colored by the fact that my experience is mostly in the San Francisco tech scene.
My observation is that use of R vs Python seems to hinge a lot on people's backgrounds. People with backgrounds in engineering and the physical sciences seem more likely to use Python. People with backgrounds in stats, medical science, or econ are more likely to go with R.
