Hope I can offer some advice as a vet.
The individual products have advised routes (eg. intramuscular, subcutaneous) as this is what they've been tested on, and they are absorbed into the blood stream at the right rate and concentration to do the job they're supposed to.
Most antibiotics (but check the label of each one you get given) are given into the muscle, because this gets them to a high concentration in the blood faster than under the skin.
To give a lamb an intramuscular injection, I usually fold the back leg up, so that the thigh is big and fat, and inject into the front of the thigh, this usually avoids all the big blood vessels and nerves. Occasionally there will be a spot of blood because there are small blood vessels in the muscles and the skin, but shouldn't cause the lamb too much discomfort.
For a bigger lamb or a ewe, there are two good options, one is again the thigh, part the wool as best you can and find a spot that feels like fairly solid muscle over the thigh, it should feel like poking your own thigh or bicep. Alternatively you can inject into the neck because this is away from the better cuts of meat in the back legs if you are sending animals for meat. Again, part the wool, and find a spot that feels like muscle. Aim for the top side of the neck, rather than the throat, as you will avoid the windpipe and the big blood vessels in the neck.
It is advisable to try and suck up a bit with the syringe before injecting, as this way you will see blood coming into the syringe if you accidentally hit a blood vessel. This is not a problem, just pull the needle out a little bit and point it a bit to the side, try again, and if it's all clear, then inject away.
Subcutaneous injections are often done in the skin of the neck as well, and this is a common route for vaccines, as you want the injection to hang around a bit longer, and expose the animal to a little bit of the vaccine for a long time.
The best way to do it is to lift the skin, make a tent, and put the needle in at the base of the tent, checking it hasn't gone through the other side. I usually stand behind the ewe at that time, because then she can't back away from you.
Not many injections are expected to go under the skin of newborn lambs, but there is a lot of loose skin, just find a bit you can get hold of, and pinch up into a tent, again putting the needle in at the base of the triangle and checking the other side to make sure the needle or medicine isn't coming out.
Hope that helps
