Quit cold turkey. I know you probably don't like for other people to call you out and tell you about the tough things they have done, but I quit marijuana, alcohol, fast food, soda, and pizza all at the same time, while also changing my erratic sleep schedule to a normal one and starting to exercise.
Think about it this way, if you get through it, you will have a huge feather in your cap, as well as becoming a lot healthier. If you fail, it is only because you allowed yourself to fail. Most people fail without trying. They tell themselves things like "I'll never be in shape" or "I'll never be good at sports." They are correct because they have made up their minds. You've already passed that step and decided to quit. The next step is to have the self determination to pull it off.
If you have to, take Excedrin. It has aspirin, acetaminophen, and most importantly, caffeine. It will ween you off the caffeine while taking care of your headaches.
Think about it this way, if you get through it, you will have a huge feather in your cap, as well as becoming a lot healthier. If you fail, it is only because you allowed yourself to fail. Most people fail without trying. They tell themselves things like "I'll never be in shape" or "I'll never be good at sports." They are correct because they have made up their minds. You've already passed that step and decided to quit. The next step is to have the self determination to pull it off.
If you have to, take Excedrin. It has aspirin, acetaminophen, and most importantly, caffeine. It will ween you off the caffeine while taking care of your headaches.