I've been given the task of redesigning the h1 headings on a travel website and have no idea where to start with obtaining some kind of secondary or primary research to get some useful data to drive how the redesign should look. Does anyone have any suggestions where to start?
Start with defining the problem. Why are they being redesigned? Legibility? Does the CMS let people but in too much text so they break the rest of the design? Are they confusing (users don't understand them)?
That said, I think you're going to struggle to find much research that's Header specific. I'd look at generic Typography research on ways to improve legibility, proportion and vertical rhythm.
Like what Luke said, you need first to define the problem. Because what's the use redesigning the H1 Header, is the font size of H1 is too big? I suggest you look for all the elements/words where H1 is being used. So once you've change the size, you make sure that it's appropriate with other pages look and feel