I hate to do it but I gotta take serious issues with some of the things Shelley put forth in her post here.
Unfortunately, NIH training grants (T32 type NRSA) are not an answer to most financial woes. My graduate program had one, and I was on it. At the time, any one student could be carried for two years (I think that was a peculiarity of how our program chose to use the money) and it only funded half of our students. Considering that my program was pretty small (we typically admitted 6 per year), I have doubts about the ability of a T32 grant to pick up most or all students in a larger program that takes 10-30 students a year. Secondly, institutions can have renewal of a T32 turned down, and I think this was the case with Harvard or one of the other big-name neuroscience programs just a few years ago (I’m probably misremembering this so don’t quote me on it). Students also cannot receive more than 5 years of NRSA award money, so the likelihood of funds running out towards the end of a project are increased, and trust me you don’t want to be worried about finances at the end of a dissertation!
I also don’t know anybody who actually pays for a Ph.D. in the biomedical sciences. Most programs, even if they don’t have T32 training grants, have enough funds to float students until they find an advisor who can pick up the tab. This is usually how things are done. Plus, a good program looks after its students, recognizing that from the prestige vantage point there is a definite vested interest in seeing qualified applicants finish and get high profile placement in the workforce.
Even if you don’t attend a high-profile program, it doesn’t matter all that much! What counts is 1. your mentor’s ability to support you and 2. your mentor’s clout. There are plenty of high-profile scientists in academic programs that are “beneath them”, but they do marvelous research and have a great reputation. As long as your mentor has street cred, you’ll get the job you want. You’re better off picking a mentor who can teach you the best science than you are picking a high-profile program with nobody you find interesting enough to work with.