The choice of font you use at your website can be affected by so many different elements: personal taste, style, screen resolution and size, operating system, monitor age, background and - not last - readability and ease of use.The most common font used for print ant Web is Times New Roman. This is default font of many applications including most of Microsoft Office Suites. That is not to say it's most readable or comfortable font; on contrary, Arial, Courier and Verdana are considered more readable.
A study conducted at Wichita State University in 2002 titled: A Comparison of Popular Online Fonts: Which Size and Type is Best? found these amazing results:
Times New Roman was deemed least preferred font in 10 or 12 point size.
Arial was most preferred in 12 point size and Verdana was most preferred in 10 point size.
Overall, Verdana was most preferred font for readability and ease of comprehension.
The fonts considered most legible are Arial, Courier and Verdana.
As far as looks, Times New Roman and Georgia are preferred over others.
All above appears to imply that for design choices, like when a large font is used as a decoration, Times New Roman or Georgia is choice.
For general speed of reading and less strain on eyes it's Arial if using a small font.
Verdana was choice for best compromise between legibility and speed.
All above should be included in building plans for your website since they can affect looks of so many items, such as: Headlines, header tags, choice of colors, links, contrast and decoration.
You can compensate for many elements of styling by using different fonts and sizes. For example, if you are super imposing text upon a graphic perhaps it would be best to make font bigger to help eye separate font from image.