When creating a web page you still have to pay attention to your typography. Working on the computer and designing a web page that is easy to read and pleasing to look at come with a whole new set of things to look for.
The biggest thing to pay attention to is that the computer you design it on, is not the computer that it is getting viewed on. Screens are all different sizes and show colors that won't be exact to yours. Make sure you structure you page with divs first and then keep your type within them so that they can't be cut off.
Also, be aware of your options of type faces. Not every type you know will be there and even if it is, not all computers can see it. If you pick Arial and that computer can't view it the next that will show up is Helvetica, and then any Sans-Serif. So it's important to make sure that your design will look okay with any of these Sans-serif.