I hear “soldier” and I assume you’re in the army. I can assure you that some random airman (such as my brother), let alone Marine, would NOT like that assumption.
“Service member” or “in the military” are a bit clumsy, but better than applying one service’s term across the board, what with all the mostly-friendly rivalry between them.
Serviceman/woman does seem to be the generic term (insofar as there is one!). For your interest and fighting ignorance, in the British Army things get a bit more complicated than this, mostly due to regimental traditions. Thus, a member of the Royal Engineers is generically referred to not as a soldier, or even as an engineer, but as a Sapper; members of the Rifle Brigade are ‘Riflemen’; other titles include Craftsman, Fusilier, Trooper, and Gunner (for my own regiment, the Royal Artillery).
The generic term for a group comprising members of many different regiments remains soldier, though.
I never really liked being called a “service member” or referring to “service members” in general. I’m just childish enough to immediately visualize a large formation of penises, all standing at attention.
If you don’t like “soldier,” then “service men and women” is good. “Service men and service women” seems a bit lengthy, and “service people” or “service persons” seems too PC for me.
I was a U.S. Navy Seabee (Naval Construction Force), and as such we were neither fish nor fowl (so to speak). “Squid” didn’t apply and I never really heard any cute interservice name for us. Usually, it was just “fuckin’ Seabees”, usually said with either a tone of admiration or a sigh of disgust.