Research weight will depend on the program. Look at the faculty, which will tell you a lot about the program's mission and ideals. Programs tend to want to train people in their own image. A few papers would be nice if possible, just because it demonstrates your ability to follow-through on projects and it gives us an idea about your overall interests. But its definitely not like every interviewee at MGH or Columbia has a PhD and a Nature publication.
You can do just fine without much research background as long as you don't walk around telling everyone on the interview trail that your plan is to become a fully funded clinician-scientist at a major academic hospital working 6 weeks a year and spending the rest of your time in the lab. People seem to think that's what we want to hear, but in reality few people get to do that, and most of them have a well-informed research direction by your stage. It actually makes us nervous because our goal is to get you where you want to go, and setting up unrealistic expectations is a recipe for failure. It also makes you look like you don't have a clue about how the world works.
So if you're a middle author on two low-level papers on liver metabolism from medical school and have one abstract from AAN about a residency survey you did, don't go telling everyone on the interview trail that you want to write a K08 application for interrogation of SAH inflammation pathways using optogenetics. You can be interested in research, you can be involved in research, and you can be a site-PI for clinical trials and run observational studies without NIH or equivalent funding. For a lot of people in NCC, that's sort of the norm, and you can cultivate those interests during fellowship so you can eventually run projects on the things that interest you during your career.