Tools you need to develop the Joomla! extensions
Obviously you need a computer to develop Joomla! extensions, but the type of computer you choose is completely up to you. There are free open source software for all the major operating systems, but the most popular operating system in the Joomla! community from my observations at Joomla!Day events seems to be Mac, although personally I use Windows, and there are those that use Linux too. When it comes to Joomla! development, there is no advantage of one operating system over another; you should choose whatever you are most comfortable and familiar with.
You will need to set up a local development environment with a web server, PHP and MySQL, however there are many ways of achieving this. XAMPP