There's a good chance you're already using the ever-popular Evernote. And you should: it's perfect for storing your research, no matter the shape it might take: Evernote syncs text notes, photos, scans, web pages, and audio recordings between devices and makes them searchable, and for that alone, it's a must-have.
It's probably less popular as word processor. There are a slew of other options, including Apple's fully featured Pages and minimalist apps like Writings, type, and Daedalus, which promise a distraction-free environment. I've tried most of them and always returned to Evernote for my on-the-go drafting needs: it's already on my home screen, it has just enough features, the full screen mode is clean and simple, and it syncs automatically. And if you have a premium account, it keeps a history of your notes in case you want to roll back to an earlier version.