This comes up here a lot.. so have a search and a read around
But to get you started, Theres a few types of airbrush;
Single action
and
Dual action
You want Dual. This means the trigger pushes down for activating the airflow, and pulls back to release paint, and its variable mid use.
Single action ones just have a on / off type trigger with preset air and paint levels.
Next theres gravity feed and siphon feed types.
You want graity for painting mini's generally, They operate at lower pressures, with thinner paints, and can get more detail because of this. Our 'job' is a very small piece as far as items to spray usually go so a 'detail' airbrush is what we want, and its not really going to do details easily at our scale. Theyre very very good for basecoats, blending colours, varnishing, preshading and the likes.
Skilled hands can get in there and pick out tiny details but tis really very hard to do at first, so dont expect to replace your paint brushes.
You want a tank on your airsource really, it helps with even airflow and is more on demand than operating without.
A little hobby compressor with a couple of litre tank is plenty. Airbrushes dont use huge amounts of air, your looking at 10-20psi for most jobs really.
Nozzle size affects how thick a paint you cna spray through it, and how much detail you can get.
Really small ones are fussy about having good paint going through them (pigment particle sizing and paint medium viscosity)
Go for medium... 0.3 to 0.4
mm should be a happy medium place.
Your going to need a cleaning agent for this airbrush, dont use anything with vinegar in (read household glass cleaner - use automotive glass cleaner if you want) it as it will strip chrome in no time. I use 99.9% Isopropyl alcohol mostly.
Your also going to need a thinner, I reccomend Vallejo Airbrush Thinner. Its the bees knees!
Another good one is Liquitex Airbrush Medium. It was the bees knees untill I tried the vallejo one! (still not bad though)
Also... read around and research. Theres some amazing airbrushers on youtubte. Most of them dont paint models. So check other applications for good usage tips.
e.g cleaning your airbrush is the exact same procedure in any application.