That Finance MP is significant, I think, because I don't think they give out many MP. I'm "old Army," too, so this is all pretty new to me (we just asked for active duty and put branch preferences in, and, IIRC, found out everything at the same time; there were no interviews, branch commandant rankings, etc.), but if Finance is his first choice, and they gave him a MP, I'd recommend he go for it. In the -- I think somewhat unlikely -- event that he didn't get it (which I think would only be triggered by too many cadets above him in the OML with Finance MP asking for Finance #1), then they'd move him to his #2 rather than relegating him to reserves. I'm pretty sure about that, but I guess he should confirm with his PMS to be absolutely sure. What I would NOT do, unless of course this is what he wants, is branch detail with Finance to follow. Because if he does that, then I'd bet that's what he'd get rather than Finance straight off. This is because Finance traditionally branch details a lot of their officers.
Sounds like our sons are somewhat in the same boat. Mine got MP for TC, QM, and Ord (the log branches, which is what he wants), and I recommended he just order them 1, 2, 3 in whatever order he preferred. I hope that's not bad advice, but if you put your MPs 1, 2, 3, and don't get one, then the system doesn't make any sense. . . .