Tax dollars at work! The U.S. government has published draft visual style guidelines for web sites. You can download their font files and color swatches. The guide is intended for government web sites, but you can also apply the same advice and resources to your brochures, white papers, presentations and, yes, web sites.
Aside from the free downloads, the online guide shows you how to pair fonts and colors for attractive, readable and accessible designs.
For ideas about how to apply these fonts and colors to various page layouts, check out the NASA Graphics Standards for information on page grids.
This visual guide recommends the fonts Source Sans Pro and Merriweather for typography. These are open-source fonts that anyone can use, and available in the download. (These fonts are intended specifically for online use, unlike the Microsoft Office fonts that I recommend for printed documents.)
These design elements conform to section 508 for accessibility. The government requires that information technology developed, procured, maintained, or used by federal agencies be accessible by users with disabilities. You may not need to adhere to section 508 in your social and public sector work, but it doesn’t hurt if you get it for free.
Beyond the visual style guide, these guidelines contain a bunch more stuff about web page design, the vast majority of which you likely won’t need. But if you’re making a web site or blog with free tools like WordPress (used for this site) then you might find the additional guidance useful.