A decent IDE and browser are really all you need to develop Windchill customizations. [You can actually skip the IDE and use a text editor and the command-line, but an IDE is really, really helpful.]
There are, of course, also plenty of other tools that might be helpful, e.g. various free browser plug-ins, but you can add these as/when needed.
That said, any software that is going to be more than a temporary experimental hack should have a consistent, repeatable, and reliable build and deployment process. Ant (which ships with Windchill so it's not really an extra tool) is often used in this context, but there are other tools, of course. One of my old managers used to say that the software "doesn't exist" until you have a repeatable build and deployment process -- and he was essentially correct, without this you might not have software or you might have unpredictably different software on any given build/deployment.
Further, any substantive software development really should use a version control system to manage the source code. There are plenty of free and commercial solutions in this space.
Finally, I'd argue that it's worth considering some sort of version control on the deployment itself -- thus allowing rigorous change tracking there as well as facilitating deployment/update across Windchill instances or cluster nodes, though rsync or robocopy can be used in this regard as well. Not having a clear sense of what changed and when in one's deployments makes it far more difficult to identify possible causes when the system suddenly starts misbehaving in some fashion.
