Are you a prior Lance Corporal who then transitioned to a corpsman and now becoming a physician? Ironically that is my exact pathway since 2003. Congrats on the adventure thus far!
Anyway, very easy to get green side orders if you want them in the Navy. After internship you can request to do a GMO tour (not always everyone's first option therefore you will have prime pickings) and you can request a green-side billet from your detailer. If your plans change and you don't necessarily WANT to go out for a GMO tour, you may have the opportunity to go straight through in to residency. If this is the case, and you are still interested in green side work, your specialty really needs to be primary care (ideally FP or ER). There are members of every specialties who have green side billets these days (we even have ortho green-side billets), but they are not necessarily your "operational billets" that GMO's and primary care can fill.
If I can offer my two cents... Don't focus on just one thing, especially if you are entering a pathway through military medicine. Your interests, passions and life can change along the way and you should let that happen naturally. Initially I was in the same boat -- I wanted to be primary care, green side, Oorah doc. I then realized a surgical pathway suited me best and then I realized ortho was where I fit. Still, I was highly considering requesting a FMF billet as a GMO. I landed my ortho internship and was then offered to go straight through in to residency. An offer like that you can't turn down (you can, but it would be a very personal decision). For me it was a career decision, family decision and life decision to finish ortho residency as fast as possible. If you truly want to do something you can almost always make it happen after you are specialized and with more rank on your collar (i.e. if I still want to ground pound with a green-side medical billet I could, even as an orthopedic surgeon).
Hope that helps!