I believe most of the military personnel for the atlantis
expedition were marines. Shepard as far as I know was chosen for the expedition simply because he was able to use the ancient technology. He was chosen for overall command of the military personnel because of his grade, not position; major outranks a lieutenant.
As far as the difference with marines they were probably chosen because Marines are organized into expeditionary forces, designed to start from a "beachhead" and expand outward. Their biggest strength is their mobility without as much heavy equipment and being able to hold postion without a lot of armor or equipment or backup, I imagine that has much to do with why they are chosen.
I always kind of thought it funny that the air force was the primary force in stargate. I understand why it was chosen, being a space type mission is an air force thing, but as far as air force special forces, they are designed for either combat search and rescue or for scouting targets before, during and after aircraft strikes, not for what they are used for in the movies and shows. I would have expected specially trained rangers or delta operators, but that is just me.