I find using Nitrile gloves while airbrushing is essential. Like Jakko, I use one glove on the non-airbrush holding hand while painting. There's a lot of concern about inhaling paint and thinner vapors but these chemicals can be absorbed through the skin too. Nitrile gloves are also non-allergic (hypoallergenic). I also use these gloves for handling model parts when I don't want fingerprints on the model.

I use the blue 5 mil Nitrile gloves from Harbor Freight for $11.99 per box. These come in boxes of 100 in sizes small, medium, large, XL and XXL. I use the smallest size that I can comfortably get my hand into so that they fit snuggly at the fingertips. I've found that small details can be felt through these gloves although the 3 mil white Nitrile gloves that Harbor Freight used to sell provide the best touch sensitivity.