You will need a different set of tools depending on your the area you want to focus on. The basic set of tools that a web application-focused hunter will probably need to get started are:
Bug bounty hunters use tools all the time to automate certain tasks, but as you progress it is important that you start writing your own scripts to cover specific tasks while hunting. On top of that, it is important that you do not rely on your tools, make sure you really understand what you doing with the tool. At the end of the day, you must take control of the tool, and not let it take control of your abilities. For a comprehensive list of tools, Bug Bounty Forum put one together here.