I think it's also important that the research you do should fit into your application. Here's what I mean:
I'm reading an application and it looks like this applicant has a strong interest in public health. Every single thing they've done is consistent with this interest except for the fact that they spent a summer doing research on Wnt signaling. They didn't do any public health research. When I read an application like this, I'm thinking, oh, it's nice, they've done some basic science research. But I'm also thinking, this isn't consistent with their interest in public health, as I would have expected them to do some public health research.
So there are two possibilities: either they were interested in basic science research, so they tried it out (which is awesome and perfectly cool), or they were just going through the motions because they thought they needed basic science research to get into med school. In cases like this, I ask the applicant about their research during the interview, and I try to see why they did it. If I get the feeling that they did it out of interest, I make a note of it in their evaluation (which is a good thing). If I get the feeling that they just did it to get into med school, then I make a note of that in their evaluation (which is not such a good thing, since it basically means that I think it's meaningless).
Then there might be an applicant who is super interested in science, and everything in their application is consistent with this interest. And they've been doing basic science research for the last 3 years. For applicants like that, I don't really probe for the motivation, since the application speaks for itself. In those cases, it reflects positively on the applicant.
So, to summarize, research is something that is definitely looked for, especially at research-intensive schools. But I don't think it's simply the presence of research that is important. It's the presence of research that is either consistent with your application, or clearly motivated by interest rather than an attempt to get research on your application. So if you're interested in basic science research, do basic science research. If you're interested in epi, do epi. If you like math, do math research. If you like public health, do public health research.
Just think about it, most of the people who read your applications are not going to be snooty people who are looking for all of your faults. They're just looking for consistency, because it's remarkably easy to get a feel for a person (and the quality of their work) if their application is consistent.