For the most part, font selection for the Web is limited. There are only a select few fonts that are available on all platforms, and even when we say cross-platform fonts, we really mean just Macintosh and Windows. We forget all about Linux, other desktop operating systems, and portable systems as well. Personally I tend to reach for Verdana, Georgia, Trebuchet MS, and Lucida Sans. Verdana is probably the best choice for web fonts and more preferred than Arial. I like to replace Times with Georgia as well, as Georgia looks cleaner and more distinct to me than any of the Times fonts. For medium to large headings Trebuchet MS and Lucida Sans are more appealing, than Verdana.
To learn more about type for the web, read Joe Gillespie’s All You Wanted To Know About Web Type. This article from Web Page Design For Designers is still a must read for web page design.
Once you know which fonts to use, you need to know what CSS can do for you. Garrett Dimon’s CSS Typography mentions some concepts to keep in mind when styling fonts. The most important idea to grasp being that white space and headings make web pages easier to read.