i'm no expert and i really don't know what the fellowship selection committees are looking at in choosing candidates for interview. however, here is my take:
to do well during residency and get letters from folks, at least one or two from hem/onc attendings, who know you well and can comment on the areas in which you excel and the attributes you possess or skills you have demonstrated that would make you a good hem/onc doctor, let alone a good candidate.
i think where you do residency matters. the bigger the name, the more doors open. that's not to say going to not-so-top-tier schools is a liability. your application and letters should speak for itself (well, i'd like to think it goes that way). bigger programs have more leaders in the field and this may or may not translate into research opportunities.
i do think my rejections from places like dana-farber and ucsf stem from my lack of research at this point. i think it helps to have that background because some places (more than others) emphasize research to the point that they minimize your time in clinics to spend more time in the lab and writing proposals and grants for PI's. i want to get involved into translational or clinical research, so i tried to steer from the more pronounced "research" machines like JHU, MD Anderson, Stanford and U of Washington. to each his own.
finally, keep an open mind. i decided on hem/on several months into my 2nd year of residency after having done clinical work in another field i was considering. i thinking deciding on a subspecialty too early on blinds you to other opportunities and interests. all medicine should interest you as you're being trained as general internist during residency, not a pre-fellow (well, that's just my opinion).
-S.