I have some 1/2 inch syringes and pen needles (which I use for IM in other areas), but I can easily get IM in the back of my calves with a 5/16 inch (8mm) needle.
It really depends on your body. I don’t have any fat on the back of my calves, so it’s easy to get IM there. But the length of the needle really matters for each person
The rubbing and warming helps speed absorption, but faster than that is to simply use the muscle. Try the back of your calf and then jogging or walking.
For IV, I am able to use 5/16 inch (8mm) 31 gauge needles, which is much smaller than what the labs use to draw blood, so it doesn’t cause much trauma. But I am lucky in that my veins are easy to get to. Again, it will depend on each person’s physical makeup, if they have veins that are easy to access or veins that are further down.
Pen needles and syringes are available without prescription.