Anywhere that the paint is checked like that has to get taken down to bare metal. Use a good quality high-build primer, sprayed from a gun. The cheap harbor freight spray guns are great for projects like this, and will give you a better result and save you money compared with doing everything with rattle cans. The key to getting the paint to stick is proper prep and keeping everything clean. Anything that can be taken off should be removed rather than taped up. Anything that is going to be primed should be finish sanded with 220grit sandpaper, then when the primer cures the final sanding before paint should be 400grit wet. Take your time and read all the instructions on all the paint materials, and follow them to the letter! This includes number of coats, time between coats, temperature recommendations, gun pressure, etc. It isn’t difficult to do, but it is very time consuming, and everyone has a tendency to get antsy and try to hurry things up, and that will ruin a paint job.