I am installing 2x3 furring strips(16 oc) to joists in basement for hanging 5/8 drywall. Should I be using 10d or 12d or 16d nails? I guess 16d may be overkill. The joist are 4x10s with 48 inch oc. I can add 2 nails for each joist.
If 8d (2-1/2") ring shank nails are usually used with regular 1x3 strapping that's 3/4" thick, with 2x3 strapping that's 1-1/2" thick, you'd want at least 3-1/4" long nails, which is 12d.
Did you consider screws? You can get #9 x 3-1/4" construction screws such as the Spax, that go in with no pilot hole needed for < $10 / pound. I'd find it easier to handle an impact driver than a nail gun or a hammer under the joists. You can drive the screws part way on the ground, then finish them in place.
The nails you want to use would be the coated style of 16d. These are the ones long enough to go through the 1.5 inch thickness of the 2x3s and still get good purchase into the overhead beams. The coated nails (slight greenish or brownish in color) are designed to really bind in well into the wood so that they do not pull out easily.
Do not use the common uncoated type nails.