Tim,
I won't pretend to be an authority on the subject, but here is the best advice I can give:
In terms of classes, and when to take them - realize that mech engineering has some pretty difficult classes, so provided you stick with the premed track, you will have to schedule accordingly. Start of with plain and simple Gen Chem. The next semester see how you handled the previous one (i.e. if you struggled with g.chem and 1-2 math/engineering classes, then don't add extra premed work) and add additional premed courses as you go. For me, I was a psych/neuro major, and did gchem 1 first semester, then gchem 2, bio 1, and calc 1 second. Starting soph year I did orgo 1, bio 2, calc 2. These were difficult course loads, but if you can handle them, go for it. Also, realize you want all premed classes done BEFORE the MCAT. Yes, that means physics and biochem. This will make studying for the MCAT much easier.
ECs - don't do anything because someone says it will look good. The best doctors (and lawyers, business people, engineers, etc...) are those that do things because it makes them a better person. If you want to tutor, then do it. Adcoms don't have a set amount of hours of ECs that they look for. They want to know that you took something from your experiences (unless of course you lie on your apps, but I like to think that Adcoms see through that).
Medically related ECs - start off wherever you can. First, find out if medicine is what you really want. Read news about events that impact physicians, talk with physicians and find out how they view medicine. In terms of what is a good experience: My school had a large teaching hospital that I volunteered in. It was a waste of my time - I folded towels, and once in a while got to push a patient to a recovery room. I found the best experiences I had were shadowing a teaching physician that was working with MS3 and MS4 students. These students are not far removed from where you are at, they love to teach, and they have insight in to the admissions process. How do you do this you may ask? Look up the phone number of a doc and call them. Most are happy to take you on.
This is about all I can really tell you of now. Again, make sure this is what you want to do! And, good luck, post again if I, or any of the other members can help you out.
BG