Fonts are very subjective topic for most people, and it's hard to separate out functionality from asthetics.
This of course becomes more important when considering body copy, where the font has a big job in supporting the readability of the content, while also trying to convey the tone of the site.
Looking at the choices of others
Once upon a time (i.e. before web fonts) we used to have a very limited choice, so choosing a suitable font was much easier than it is today with the huge and ever-expanding range of free and paid-for web fonts.
One way to get past paralysis in the face of overwhelming choice in terms of fonts is to consider what everyone else uses. Because I don't have the time to cast a net across the entire web, I've decided to have a look at the font choices of the top 15 news sites and the top 15 blog sites. There's some overlap between the two categories, so I've also added a small handful of up-and-coming news sites such as Vox and Vice.
The chart pictured above can be found here, and the original data here.
Georgia wins in terms of body fonts (7 sites) — this is probably because of a mixture of the fact that everyone used to use either Georgia or Verdana or Arial/Helvetica in the days before webfonts, and that because Georgia is a system font it's available on most devices, without incurring the font download penalty, and also has a large range of glyphs
Open Sans is the leading webfont used as a body font, which is cool as it's a great font, and is getting plenty of use by the likes of Google
Helvetica Neue is popular both as a display and a body font, and some sites — Yahoo News, Fox News, and CheezBurger — use it for both, meaning a quicker download, than if using separate fonts for body and display
Although Helvetica Neue is significantly different to Helvetica or Arial, all three get used for both display and body copy, and taken together, make up a big chunk of the dataset
Only one site used Verdana, which means that it's almost totally out of favour, as it used to be pretty popular in the days before web fonts
Open Sans doesn't seem like the worst choice for a body font, and Helvetica Neue is obviously a contender also
Georgia and Helvetica / Arial are still worth consideration in terms of fast downloads, and one of the two should probably still feature in the fontstack as a fallback
Fonts do wax and wane in terms of popularity (vis-a-vis Proxima Nova), so although popular today (and remember that this survey is only considering 32 sites), a given font may drop in use quickly over time. However, as far as web fonts go, Open Sans and Helvetica Neue both seem to have a lot of momentum (e.g. Helvetica Neue being used as Apple's OS font).
Compare TypeWolfs most popular fonts of 2013 with their most popular fonts of 2014 to see how quickly fonts can rise or fall in popularity.
MyFonts also have a nice post on the most popular fonts of 2014.