Accepted answer
20 units is 0.2 mL, which at 3.33 mg/mL is 0.666 mg. Work it in that order and there is nothing to guess at: units to volume on the U-100 scale, volume to dose through the concentration. Draw with the barrel vertical, expel the air before you read, and read the leading edge of the plunger stopper rather than the shoulder — the difference between the two is about a unit on a 0.3 mL barrel.
Start with the barrel size, because a 0.3 mL barrel graduated in single units and a 1 mL barrel graduated in twos are different instruments for this purpose.
Needle length for subcutaneous administration is conventionally 4 to 8 mm; the 4 mm length is sufficient for essentially all adults and reduces the chance of an intramuscular injection.
U-40 syringes still exist, mostly in veterinary supply. A U-40 barrel marked "20 units" holds 0.5 mL, not 0.2 mL. Using one with U-100 arithmetic overdoses by a factor of two and a half.
Graduation intervals by barrel size are printed on the packaging and are the practical limit on dosing resolution.
Half-graduation estimation is not measurement. If the dose needs it, change the concentration instead.
Smallest barrel that holds the dose. Resolution is free and you should take it.