Traditionally a sans-serif font is chosen for main content text for websites that want to provide a "modern" looks (current apertus.org wbsite uses Droid Sans - new website screendesign was envisioned to use Roboto). Serif fonts are also traditionally mixed in for header elements or other graphics elements to separate themselves from the rest of the text content (currently we use Oswald Light on apertus.org).
http://fontjoy.com/ seems to tackle exactly this font matching challenge.
Not convinced we should use Titilium (which is our apertus logo font) for main text content on the new website - for headers or certain other elements it could make sense though IMO.