There's a lot of knowledge out there about the impact font choice can have, ranging in objectivity and subjectivity. And like any sort of color study, you'll find a lot of variation... the key is to figure out what works best for your specific scenario. So in short, make an educated guess and test it.
An interesting example of a test was performed by Errol Morris on the New York Times — spoiler alert: he tested typefaces and their effect on the perception of truth.
Typically one would say that a serif font is more traditional and academic, therefore it receives more trust... but that depends greatly on what you're doing with it...
A traditional serif typeface might work really well for the New York Times because their history and journalistic rigor is a huge part of why they're a trusted news source. To contrast, a tech start-up like Uber might be better suited to use a sans-serif treatment because they want to exude modernity... a traditional serif typeface may make them feel older and less bleeding-edge, which is contrary to their brand tenets.
I think before you continue seeking guidance with your question you need to first determine what your goals are in terms of visual language for your site, and then seek research/advice specific to those goals.
If you're feeling like you have too many options, start with the most common typefaces available (http://www.cssfontstack.com/) before you decide to subject your users to additional resources (additional bandwidth adds up!).