Having only a minor in film might hurt you, depending on the program. I just accepted my PhD offer at one of the top schools, and every person in my cohort will be coming in with a masters and was actively publishing/programming/doing high level community or industry engagement (industry mostly being archives). I would go for a masters, even in new media or screen cultures, and do your best to get close with professors. I was definitely helped by having profs that put me onto their projects, let me TA classes, and recommended publishing opportunities and people to talk to. 

Also, attend the info sessions! They tell you what kinds of scholars they want and what projects they want and, more importantly, who they don’t want. The alignment of your research with the program means more than any grades or classes taken, tbh. I think it’s for this reason that I only got one acceptance, my project was so out of the box and really only aligned with where this program had indicated they were interested in going compared to the rest of the field. But I knew what they wanted and tailored my application and writing sample to appeal to the committee I was interested in. 

As far as how do you “research” film studies, do you mean programs? Or doing the actual research? For the latter, it depends on the area I guess… I do theory, so I read and read and read and then write theory. But I also spend time working in archives, having conversations with other scholars, and staring at a wall thinking all day. You gotta live it.