As you have read, there is no right or wrong answer on this topic, just plenty of opinions. I highly recommend using whatever works best for you.
I personally use a 5 gallon air tank with a regulator and oil/water trap. I fill the tank from a small compressor in my basement. The tank can be pressurized up to 125 psi, but my compressor has never gotten it over 105 psi. This is plenty to paint a car (interior and exterior), tank, or plane (I prefer to hand paint my figures).
I have tried some of the compressors made for airbrushing with mixed results. Some give a pulsating air supply which I find very annoying. As long as I have enough air in my tank, I know I will get a constant pressure with no noise. I haven't tried the CO2 as I don't have that much space in my model room.