Biostatistics vs Statistics
I'm assuming you have a math background?  If so, I would say go with regular stats and see if you can gear your course of study more towards the medical side of things (by taking a course in epidemiology or other medically related courses, and doing a research project in the biomedical field).  I think you will leave more doors open this way.  I think that Biostats is generally geared more towards biomedical research.  You collaborate with doctors and scientists.  Taking statistics would allow you to go this route if you desire, but also leave doors open to the quantitative social research/data mining that you mentioned in your post.  Then again, take what I say with a grain of salt.  Do more research on each subject to find out what is best for you.