Academia has always been a bit of an elitist field, and will always be. For this reason you'll get the best chances by attending brand name universities and doing well in them/getting yourself published in their research. The pedigree is very important.
Other than that, which speaks more of the idiosyncrasies of the gatekeepers than of the quality of work that can be done, just your drive should be enough. You could go to one of the lower tier schools and thru hard work and dedication, foresight and intelligence, become a phenomenal researcher/academician. It would simply be easier if you were to attend schools like JHU, HMS, P&S, Stanford, UCSF, etc...
Also, I have heard that it helps to shoot for a residency in a large academic program (affiliated with a university), rather than a community based program. Again, not that it is impossible if you attend the community programs, just that it becomes a bit harder...