I was curious if anyone would clarify what kinds of Medical-based groups there are in the shadows and exactly what they actually do?

I'm making a very Mercinary medic and would like to have a better idea of the groups he may come into contact with.

Read Neuromancer, particularly the bits that talk about Ms. Chin and Case's and Molly's experiences with "black clinics." Your most basic form of medicine in the shadows is the street doc. He's exactly what it says on the tin: a doctor (often of questionable qualifications, ethics, etc.) who caters primarily or exclusively to street-level clients. Runners, gangers, and so forth. When several street docs get together, pool their resources, and open a group practice, you have a black clinic: a secret, often hidden facility which advertises only by word of mouth and specializes in medical procedures which are questionable or outright illegal. They patch you up in the aftermath of a run, install illicit augmentation, basically fulfill the needs of "deniable assets" like shadowrunners.

Tanamous is one group you may interact with, just off the top of my head. Parts is parts, right? A "very mercenary medic" may run into them to buy or sell stuff, with some regularity.

Augmentation is going to give you some info on the major players of the medical world. If your guy is based out of Seattle, Seattle 2072 has a great deal of info from years past spliced into it, so there are tons of lists of street docs if you want specific names and addresses.
If he is proper mercenary, then you might want to pick a war zone or war zones in which he has worked. I like the Tsimshian conflict, but if the game is set in 2073, then Bogota might be the way to go.

Loose Aliances (SR3) detailed the Anarchist Black Crescant, IIRC. They are kind of an underground red cross/red crescent. The related anarchist black cross is less focused on medical aid, IIRC.

EDIT: Vice also describes Tamanous and other organlegging organizations (Tamanous, the Mansure Brothers in India and some other group that i forgot are the big global players).

I'm surprised no one has mentioned any of the various Doc Wagon/Crash Cart clones. The "burnt out Doc Wagon combat medic" seems to be a favorite back story for medic PCs.

Well, I created "Sam's Surgery and Deli", a Shadow Clinic that operates mostly for emergency services and check-ups for the SINless and the folks that don't want to explain to the nice Officer Friendly why they have the bullets inside of them.

One of the "Doctors" is a retired Marine Corpsman known only as the "Corpswoman". Not exactly a doctor, but she knows her way around knife, shrapnel, and bullet wounds, as well as mental trauma.

You mean Navy corpsman. The Marines don't train their own medics.

They might not in real life, but they very well might in the CAS, UCAS, or a half dozen other countries in 2073 that would call some unit "Marines."

I'll go with "It's the Sixth World" explanation as opposed to my own ignorance.

I honestly do try, folks. But I'm just a Civvy Puke, and freely admit it.

Navy Corpsmen are some of the best friends you can have in the Marine Corps. And they are also some of the worst enemies you can get. Woe be unto the Marine who beats down a Navy Corpsman. It really sucks to have your shot records lost just prior to deployment. Doubly so when they dull the needles prior to injection.

Does that actually happen? I mean, are there jarheads (no offense) stupid enough to beat on the people providing their medical care?

There are indeed jarheads (No offense taken) who are stupid enough to beat on the people providing their medical care. Both of the consequences I listed above actually happened to individuals in my unit. Bent needles are quite vicious when they are ripped out of the tissue they are forced into. Really sucks when the Individual who had to get all their shots redone prior to deployment got them all with bent needles. As in, the Needles were bounced on a hard surface until they resembled a small hook. Can't say that I felt to sorry for the fellow though.

Street doc: Loyalty 6 and keep it that way.

Heh...

Never underestimate human stupidity. Never!

This cannot be stated often enough.

And if the person who fixes/installs your cybernetics isn't the same as your street doc the same goes for them. Unless you want your cyberarm to flip the bird every time your cybereyes spot a cop or a ganger.