Use Roboto.

Premise

(The following refers to text designed for continuous reading)

We spend every day reading. We read text messages, emails, articles, books (jk), menu options, tab names, titles, searches, whatever. We read a lot.

Now let's say all those mediums use the same 5 fonts. That outlines the consumption patterns of most people. Does it actually matter how "good" a font is, as long as it's familiar?

A Brief History

In the beginning there were scribes. And the scribes all wrote in cursive (as in, they didn't lift their pens), and also only really had the upper case. Our first documents printed on the printing press followed the trends they set (and so do current typefaces, in many ways).

Do you think if we gave a literate reader from 1455 a modern book, they could read it? If at this point you are still not convinced, I offer you the chance to try to read a document from 1455: (source) First page of the first volume of the Gutenberg Bible, 1445

(Ironically, in a twist of history we can read older Roman texts far better thanks to the Renaissance.)

So what?

Back to our premise: if you have someone who has only read in a few fonts, the easiest way to make your site/pdf/whatever readable is to use one of those fonts.

Use. Roboto. (Or don't, this site uses a simple sans-serif flag, as does wikipedia)

Extras

I hope the more subtle point was already conveyed, but I'll make it more explicit: the most readable typography is the most common typography.

I'm sorry LaTeX/Troff/whatever users, I like a really spicy justified document too, but nowadays most people are reading left-justified/ragged sans-serifs, maybe it's time to adapt. (If you're wondering why sans-serifs are more popular, I believe it's because they render nicer over a range of DPIs.)

Further Reading