I have never owned a air driven type nailer before. I was needing to run a finish nailer and a hardwood floor nailer.

I have a Craftsman 125 psi 4 gal air compressor.
(Direct drive / 2.4 scfm 90 psi / 3.7 scfm 40 psi - model 921.166380)

My question is: Will this compressor work for me?

yep just be sure to start the air pressure around 85lbs and see if that will seat the nail/staple flush in the seat of the tongue. Adjust accordingly a few lbs at a time till its right. Dont go over 100lbs or you can damage the internal seals of the nailer to the point it wont air hold anymore.