You should be able to use whatever operating system you want, as long as the other required software can run on it. We develop on Linux and Windows, but have reports of systems running on MacOS X as well.
Of course you need a webserver. Again, you should be able to use any webserver you like, as long as it is supported by PHP.
We strongly suggest to use the Apache webserver, though, as it is the webserver used during development.
Oh, yes, you need this, and you need at least version 4.2, newer is better (although we don't have checked it with PHP5 yet!). There are only a few things you need to take care of when setting up your PHP, and the install tool will point out any errors it detects.
Of course you need PHP support for your database, and GD library support is nice to have for some modules. You do not need PDF support of any kind, we do this with pure PHP.
We use ADOdb for database access, so we are in theory able to support a large number of databases.
Practically only MySQL and PostgreSQL are usable right now, so if you need to use a different database, get in touch with the developers (or give it a try yourself).
On the clients about any modern browser will do. MSIE and Mozilla (as well as Firebird, Galeon, ...) are well-tested, Konqueror and Opera should work as well. There are known issues with Safari, though.