There are a lot of things that you have to think about when you are designing website, one of the more overlooked is the font to be used. There are basically five types of fonts that you will want to use on your site and each of these can be broken down further into sub types.
The most commonly used of the fonts is sans serif which is the one that should be used for the vast majority of the content on your site. This is a font that is easy to read on a computer monitor which is of course something that is of critical importance when you are designing a web page.
The next type of font that you will see used commonly on a website is serif. This is the type that is most commonly used in the print world since it is the easiest to read on a printed page. Unfortunately it does not translate well to the computer screen so it can be hard to read if you use it for the majority of your site. Serif is best used for pages that are intended to be printed out since it will give the best appearance to the printed document.
Another font type that you will come across in web design is monospace. This is the type of font that you should use when you have content were the spacing is important. Pre-formatted text is the most common use for it. You will also want to use it any time that you have to display code on your site.
A script font can be used in situations where you need to have the look of cursive writing, like for a signature. This can be a great way to add some style to your site by giving it a unique look. That being said you do have to be careful not to overdo it. Script font can be hard to read and not all computers can display it so you will need to limit the use of it. You will also likely want to have a sans serif backup for the visitors who have computers that can't display a script font.
Fantasy fonts can be used to add a unique look to your site but you have to be very careful about using them. They are mostly used for headings and in places where you want to have an artistic look. The problem is that fantasy fonts are the least commonly used type so you will find that there are quite a few computers that can't display them. They can also be hard to read. Again you will need to have a sans serif alternate for anything that you do with a fantasy font so that the people who have computers that won't display it will still be able to use your site.