An interesting topic: LUG had a few things (hand held shields and stasis stretchers) that would make for better general battlefield conditions, in theory. I think why you never see much combat medicine in general in Trek, at least NG Trek, is that, according to some sources, the FED isn't in the war business anymore, which is ridiculous, imho. All we ever hear about in NG is recent battles/wars with other powers; so if there is fighting (and don't tell me it's all ship to ship: O'brien was ON Setlik III, not in orbit), there would have to be somethin akin to a MASH/Forward Aid station, and that would also mean medics.
I've been thinking about evac of the wounded. I know transporters would do most of it, but since it seems like just about anything will block a transporter signal, perhaps smaller shuttle craft or some other vehicle may be used.
But, in regards to the basics: I've noticed on NG espcially, some kind of lean toward 'the old ways'. In one scene in an episode, Crusher must instruct a nurse on how to make a splint, since the bone mending device is offline, and in others she prescribes warm milk for sleeplessness (I bet your real DR. would NEVER do that...Lunestra and Amien are waiting for you....), so maybe a SF officer would get the same kind of basic first aid training that we might get.
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth