Dry air or nitrogen might have a slight advantage, but consider that 'plain' air is mostly nitrogen in the first place. Nitrogen is a slightly larger molecule (N2) verses O2, which is one reason why some prefer it. H2O expands and contracts more with temperature changes, but the real effect is probably noticeable at a track, but in typical real-world use...it's not worth the effort.
The amount of moisture in the air pumped into the tank can promote some rust...but, once all of the O2 is used, up, things cannot continue to rust! Most of the rest of the stuff in 'plain' air are relatively inert, and not likely to cause a problem.
IOW, in an ideal world, yes, it might be best to use nitrogen or dry air (this time of the year in many places, it's already quite dry), but the difference long-term is not likely to be measurable by the average user.
FWIW, to properly adjust the precharge in the tank, you need to shut off the pump, open a valve and let all of the pressure bleed off as the bladder expands. Then, adjust the precharge, then close the valve and turn on the pump...you can't accurately adjust the air pressure with pressurized water on the wet side of the bladder.