You should go bigger in my opinion. It is safer for your syringe volume to have at least twice the volume that you will inject at one time, or else you risk pulling the plunger out when you draw it. If you are backloading them then it's not as big of a deal, but I'm not a fan of doing that.
I would recommend the 1ml syringes. Anything bigger from my experience is too difficult to measure and draw up with. It is easier to be more precise when you have a syringe with a smaller diameter; as long as you measure the number on the syringe and your needle is also full, then you should get the full dose. The extra that gets lost in the deadspace is in addition to what you measured, you don't need to reclaim it.