You took a good first step. Learning how to repair or replace parts of your bike by looking up videos online gives you the knowledge for doing the job. As a bonus, when you watch the video, you will see the tools that were used. As a good first step, a set of metric hex wrenches will end up being the most frequently used tools in your kit. Tire levers for when you repair flats are also needed. Specific tools may depend on the ones needed for the actual bike that you own, for example, buying a headset wrench is of no use if your bike has a threadless headset, or buying a crank extractor if your bike doesn't need one to remove the crank in order to service the bottom bracket. Many of the most specialized tools needed to work on your bike will depend on the specific components that were used to build it.