as a full time medic, here are my perspectives (pls critique):
1) DO yell medic, so I know where to come. It's a great tracking device so to speak after I die, respawn, and don't know where the heat of battle is at. Of course, do not spam this, I usually end up "picking the call" from to the same guy who I was healing and ignore the others.
2) Uber: this I never get it right. Usually, and most effectively, it is the guy who I was healing will tell me when to uber. So, do TELL me when to uber. Now, I know, without a a headset/mic, typing would be too difficult to call for Uber (yet, I've played with one dude who can type AND play in the same time). anyway, last thing about uber, half the time I WON'T use it at the most optimal time, it is because I have low health and rather use it to keep myself alive. So don't get upset like "wtf, why did u uber just now????!?!?!?!!?" Truth is, if I am gonna die anyways, might as well use it now to keep me longer.
3) I usually heal Heavy first, it is the safest way to live; and if I am adventurous, a brave Pyro, this combo is quite devasting. Soldier is the "middle way" between safe and adventurous. Medic on Medic is kinda not efficient, since I stay behind the line of fire, the other medic is better to serve the guys who need it most on the battlefield. 2-3 per team is optimal, just as with any class (except Spy, which I think 1 is enough).
4) my worst enemy is Pyro and Demo. Cuz once on Fire, I usually have to leave the battle and leave my commrade without heal. And Demo's bouncing bomb which doesn't hit the guy I am healing, will probably hit me.
5) Multitasking: this is the meat and most important of all - to heal one guy or all.
Now, as someone mentioned above, the BEST case scenario is to heal the guys who need it most and don't stick to the same guy who has full health. However, this doesn't work quite well in the real world. Classic case: I ubered a soldier, who is fighting one enemy. Then, there is another soldier on my team who has literally zero health, so I heal him too - effectively, this will turn into a 2-to-1 battle. Win for sure. however, as i heal the other guy, the first guy thought he was invisible got kill instantly by a rocket. He then scream and yelled at me.
Now, practicing makes perfect, I do tend to stick with the same guy even though there will be others who need it more. I will try to 'multi-task' heal several ppl only when BEHIND the line of fire.
6) DO use the hacksaw. even though I love powning the guy with the syringe gun, it does pretty weak damage. For a soldier, engineer, or any "light infantry" I use the gun. Against a Heavy, Hacksaw for sure. (I have pown a heavy from behind with a saw).