Okay... I'm looking at this through 'Real World' eyes, not SG-1.
In the 'RW', you'd have next to no civilians on the project and folks probably wouldn't be living off base. It's be like being stationed on a sub or ship underway. The military services could quite probably find enough of it's own specialists in the needed fields with a small backfill of civilians, who would, basically, sign their life away. And certainly *no* civillians would be department heads, like Daniel heading Arch. The service takes care of it's own.
Also Teal'c wouldn't be anywhere near a team. He would have been 'removed' from the site under close guard, and probably sedation, and is off being "studied" [or whatever polite euphamism we're currently using] for the rest of his 'what's left of it' life.
I shudder to think of the SGC being managed by either the USA or the USMC. Both have a different mission headset and not one I think would be as easily adaptable for the job.
Now... if you consider SG-1 as a first contact team, I'd lean toward SF long before Marines on this one, and not because of team distribution, but the SF leans much more into working with indiginant population that the Marines.
Marine command would basically be the SG-3 - Col. Makepeace situation: bust in, apply sufficent firepower to nuteralize the situation and then 'hook & book'. There is a time and a place for that, but like any other 'weapon', it has a selective use.
The "A" team concept lends itself to first contact well, but is strictly combat oriented so a lot of the 'hearts and minds', 'meaning of life stuff' would not much of a place. And as we've seen in some situation, that can be important. And remember, everyone on an 'A' team is cross trained in a secondary speciality: medic may be commo, etc.
Again, this is my own opinion so I'm sorry if I offerd, but: basically the Rangers are the Army's 'Marines'. They are trained to 'go in, subdue the location and hold it until giver further orders'.
Now, before folks get cranks at me and say a woman doesn't know what's she's talking about, here's some info.
I live 15 minutes down the road from Ft. Lewis, home of 3rd Batt, 75th Infantry [Rangers] and 1st Special Forces Group. Not counting MacChord Air Force Base. 40 minutes from Bangor Naval Submarine Base, 50 from the Bremerton Naval Shipyards and about an hour from 'Home Port Everett'. I grew up here.
I served 20+ years in the Army active and reserve and did my 'winter vacation' of 90-91 in the Gulf, up front, getting a Combat Medical Badge because of it. My husband was with the 1st/509th Airborne Infantry in Long Range Recon, the 82nd, took some time off and went back in with the 12th Special Forces Group. I 'speak' Spec Ops.
Now, I have always found it interesting that you see *no* Army or Navy staff around, but, from the show's perspective, it makes sense. To keep things accurate, that's a lot of advisors. And there ae things going on in 'SF, etc that really should be left quietly silent. Being able to focus on one branch of the service keeps it easier. ['KISS' = Keep It Simple Stupid]. In the 'RW', there are probably Army and Navu people around *if* they have a speciality the Air Force can't supply. I find that chance very minor.
And nobody want's to broaden the info chain on this by dragging another Joint Chief of Staff into this. My bet is the USMC JCoS sn't aware of what's going on, just that there are some of his folks 'attached' to a 'covert' USAF project.
So... real life military situations trying to be squeezed into a 44 minute SF TV program. That is a case of where 'RL' is too gritty, rough, tedious, messy, long in planning and a whole lot more to ever make it to the screen.
{My hero of the GulfWar was 4 star General 'Stormin' Norman' Schwarzkopf when he told the reporters during one of his daily breifings that he was *not* gonna tell them *anything* about tactics and troop deployment until after things had happened becasue he didn't want 'you bozos giving the enemy my troops lives' by broadcasting battle plans. He looked out for his own.
I'd follow that man into fire.
And I did.