Most researchers just use their phone. Really hard core researchers use a camera with a tripod/monopod of some sort, to reduce blurry images from hand shake. Not all archives allow them, mine doesn't mind for example, but the one I worked at in grad school didn't allow them, so you'll want to check first before you bring it in. A string monopod is a classic budget solution. Some people use scanning apps on their phones, I don't know which ones are preferred. Whatever camera you use I would advise buying some decent PDF software and converting the images into PDFs with OCR, if they're typewritten. ABBYY FineReader is the best on the market for that.

I've used an iPad Mini to photograph archival materials for years and have found it to be very successful. What I like about the Mini is that it has a large enough screen to confirm that any text photographed is readable (not blurred), but is not so large to be cumbersome when repeating the same task for hours at a time.

One new tool that I've found helpful is Tropy. Tropy is a free research management tool that helps you sort, tag, and annotate research photos in a (relatively) easy to use app. I've only been using it for the past year or so, but I've found it really helpful on larger research trips with hundreds or thousands of photos to sort through and digest.