Safety
When I first started using the airbrush I didn't use a face mask. I figured that since I was standing next to an open doorway with plenty of ventilation, I didn't need one. But I noticed that afterward I'd have a little ache in my chest. Maybe I'm hypersensitive. At any rate I decided I'd better protect myself. So I picked up an organic vapors face mask at Home Depot for about $30. This worked real well for quite a while, but eventually it became harder to breathe through the filters. I removed the cartridges and opened one up and was surprised at how much paint had built up on it. If not for the mask, this would have ended up in my lungs. Airbrush mist is so fine that it can drift quite a ways.
I was at Coast Airbrush and asked about masks and they showed me some 3M disposables that they sell for $20. This is less than the replacement cartridges for my old mask, so I bought one. I really like it and have used one ever since. If you use enamels or lacquer and buy a mask, be sure that whatever you get is rated for organic vapors. A lot of modelers have paint booths that exhaust to the outside. I don't have room for one in my small work space. But even if I did, unless it was really good at sucking up overspray and fumes, I think I might still wear a mask. It's an easy precaution, and they last quite a while if you store them in their zip lock bag between uses. Just let them dry out for a few minutes first so you won't have a mold problem. Acrylic paints are less toxic and can be cleaned up with more friendly solvents. But I've read that even these are bad for your lungs.
Since I was protecting my lungs, I figured that having my hands in lacquer thinner probably wasn't a good idea either. So I bought some latex gloves. The lacquer thinner ate through them. I remembered from my working days that we used nitrile gloves when working with solvents. So I bought some at my local drug store. They cost a little more than latex, but are well worth it. They are much tougher and stand up well to thinners, and I can use a pair over and over. Also, they don't make your hands stink like latex. I don't worry too much when brush painting or using adhesives or putty as long as I have a window or door open. I have a small fan on my bench to blow the fumes away, and the quantity is small enough that I don't think it's a big deal. But an airbrush is something else.
Paint Booths
You can buy a paint booth that is designed for model painting, or you can build one. There are many examples and videos on the internet. And, there are many discussions on the forums, often heated, about safety requirements. Do you need a squirrel cage blower? Does the fan have to be an expensive explosion proof type? Does it have to have a brushless motor? Do you need to isolate wiring connections and lamps from the air path? Well, I don't want to get sued, so I won't tell you. But, here are some thoughts.
If you use only water based paints and cleaners, explosions are probably something you don't have to worry about.
If you use solvents like lacquer thinner and you don't allow the concentration of fumes to exceed the lower explosion limit or LEL you can create all the sparks you want and there will be no explosion. The LEL of lacquer thinner is about 1%.
It is a rare fan motor that has brushes. Most are shaded pole brushless. If you do some research, you'll find that so called explosion proof fans have non-ferrous parts to reduce the chance of sparks.
Lots of hobbyists have ignored the above precautions and used things like kitchen vent and muffin fans. I have only read one account of someone getting hurt, and it had all the earmarks of an urban legend. The author heard it from someone who heard it from someone, etc. If you have a first person account of this happening, I'd love to hear from you.