Great question, OP. To become a regular doctor, as opposed to those quacks you see everywhere nowadays, you need to get an Associate of Arts (AA) degree in mechanical engineering. Why, you ask? Well, learning about stress, strain, and deformation of materials is of utmost importance for advancing your own methods of dealing with the high pressure environment that is medical school.
Since you want to be an anesthesiologist, you should also consider a double major in evolutionary biology, since you need to learn how to be put to sleep before you can start anesthetizing other people! Doing so would greatly increase your chances for your top choice residency. Don't go for the bachelor's degree; it's so overrated and you should forget about it.
In short, your diploma should say: "Associate of Arts in Mechanical Engineering and Evolutionary Biology from Podunk University." It MUST say this! You will not have a chance at med school otherwise.