There are TONS of fonts out the to use for a business website!
I have used several over there years, an I like to make them unique and as uncomplicated as possible. By trying to avoid placing code here there and everywhere, because I tend to miss several spots, making me go cross-eyed.
Pick out a font that is clear and easy for your visitors to read, and something that you like that fits your personality. Sometimes it's hard, because I tend to like fonts that may be hard on the eyes.
If you come across a font that could be hard to read, but you really want to try it out, perhaps you can try to play with the size and color to make it easier to read.
Not every download for a font is friendly to use with the type of theme you have for your site, so just be aware of that. You may have to sift through a few different font sites because of that.
Open Sans and Roboto are now most common web fonts but they are not web safe font's because you have to host this fonts or you have to use google fonts fonts api just to make it visible to all versions and type of browsers. We'll for me choosing the right fonts are not that easy but you can try all visiting all your competitors web site and look for their logos what kind of fonts they are you using if they are serif or sanserif fonts if most of those sites are using serif font you have to search for serif fonts select the best for your site or the other way for sanserif fonts.
Well it depends on the business for whom you are making the website. Many businesses want their websites to look stylish and creative and want the designers to use various different fonts that would suit the theme of their website. However, the most commonly used ones are Open Sans and Georgia.