Been using a Badger airbrush and compressor (no tank) for models for maybe 30 years, no problems. Got a Harbor Freight airbrush to use for leather, so no potential of cross-contamination with paint thinner and alcohol used to clean them. I use 91% Isopropyl alcohol for cleaning out leather dye, and hot water for finishes such as Resolene (which I thin 50/50 with water). Always disassemble and soak the tool after running alcohol or water through it to clear out the residual. Have not had a problem in the 3 years or so that I've been doing that. Use a HF compressor that has air pressure adjustment (no tank). Haven't touched the pressure adjustment since I made the initial adjustment. I always test the flow to make sure it's what I want before spraying leather. Wipe the tip of the airbrush with a piece of tissue after you've set the airbrush down for even a few seconds, then test spray. No moisture trap, but where I live humidity is not an issue - we start complaining if it gets to 20%. I DO have one on the rig I use for models, as I used to live in a very humid environment.
The only times my HF airbrush has puked on something were from the cup, which has no lid. I chalk that up to operator error. I suggest practice on something like cereal box cardboard . A bit of dye will buy a lot of learning.