BeOS has a pretty good range of options, but not the ones you are most familiar with on Windows, Mac and Linux platforms. Out of the box, BeOS comes with a browser called NetPositive. This is a pretty good browser, with a fairly simple interface. To get a full featured graphical browser, you basically have two choices. The commercial Opera browser is an awfully good browser, with quite a few whiz-bang features for a large number of platforms.
Opera does some of the most consistent rendering of any browser with maybe the best CSS support.
The other full-features choice for BeOS is BeZilla, the BeOS port of Mozilla. All of these are good to have on hand, mostly as sanity checks on the accessibility of websites. It is worth noting that the Flash and RealPlayer plugins are available for the graphical browsers, and Java support can also be enabled. BeOS does pretty well here also, even pretty well for free. The first is a lot like the built-in SimpleEdit under MacOS or WordPad under Windows.