I’m going to get philosophical here and suggest that there isn’t one specific part that is most important to learn how to fix. The most important part to fix on your vehicle is yourself and your attitude. If you were never taught to mend your own vehicle, it can be an intimidating prospect, and breaking that mindset is the key to wrenching bliss and success! The first thing I ever fixed on my truck was the springs, I had a broken leaf spring that needed swapping. After determining that there was no way I could afford to pay for it to be done, I bought a few simple tools and managed to swap them out myself. Lo and behold it worked, and that experience taught me that anything could be fixed with the right attitude, tools and parts. Therefore, I don’t think there is any specific thing that everyone needs to learn to fix, they just need to learn that anything is fixable and to not be intimidated by working on their vehicle.