For "under the skin" injections I use (on all animals) 21Gx 5/8'', or 0.8x16mm in new money needles. I get disposable ones from the vet, use them a few times (cleaning them straight after use and then boiling them for about 10mins in water before re-use). They inevitably get bent and also very quickly blunt, especially by the sheep.
Goats get their shots while eating a treat on the milking stand, they don't really noice it; sheep and lambs is a two-person job, and I use a vaccinator gun for them (it came free at some point and works really well).
I have thicker needles for intramuscular (not to hand this minute), but you are most likely to get those drawn up from the vet already. It's mainly antibiotics.