If my experience of writing for Dogs of War is correct, translated into Traveller it should be:-
Pre-career education, term 1
Go for Medic 1, Science 0.
Assuming the dice are with you all the way and you gain graduation with honours, increase to Medic 2, Science (Biology) 1.
Graduation grants a DM +1 (+2 if with honours) to your first career, which must be Navy. For goodness' sakes, take advantage of the offer of a pre-career commission, so you enter the Navy as an O1 Officer.
Choose Line/Crew and serve with distinction. Stay there long enough to gain a rank, and then quit that job and apply for a Marine job, with the Support assignment.
If your Education is high enough, you can use the Advanced Education table to try and gain further Medic skill; otherwise, the Support assignment skills table is the only other table there which has Medic.