One of the great things about the World-Wide Web is that it and the underlying Internet are OS-neutral. You might be surprised to discover how many of your favorite websites are running Unix OS's like Linux or Solaris.
To write J2EE systems that run without change under both Windows and Unix is fairly easy thanks to
Java's "Write Once, Run Anywhere" approach. In fact, that's what I do everyday. My desktop development system is Windows, but the servers I develop for are Solaris. The WARs I create never see the difference.
Developing for Unix WWW clients is pretty much the same. I use the Firefox browser under both Linux and Windows, and while the binary executables are different, the differences in what I see onscreen are almost completely indistinguishable.
The main thing to watch out for when coding for Unix web clients is the same thing you have to watch out for when coding for any other non-Windows client. Microsoft Internet Explorer is only available for Microsoft Windows (I can't count that feeble Mac port that they finally killed the other day). IE is notorious for not conforming to Internet standards, so it's always a good idea to check your web pages with browsers such as Firefox, Safari, and/or Opera. That's true whether you're dealing with Unix/Unix, Unix/Windows, or even Windows/Windows client/server combinations.