I will warn immediately that the bulk of my experience is both fairly old and concerned applying colour to Airfix-style kits rather than any protective finish.
I assume when you say airbrush you mean an internal mix type, with a needle, rather than the mini spray gun style "modeller's airbrush". Is this single or double action? Single action have a straightforward button for the air, paint is controlled by a screw on the rear of a handle. Double action you push the button for air and pull it back for paint (you may or may not still have the screw).
Paint - don't need specialist stuff if thinned appropriately. Most paints should be fine. The only thing I remember being warned against was poster paint (not that I ever wanted it) - it's an emulsion of solids that are simply too coarse for the mechanism. Whether that is true in an absolute sense or judgement as to what I might try to use I have no idea. Thin your paint until it resembles "lazy water" - i.e. slightly thicker than water, sorry, I don't have a better way of describing it - and refine from there. Don't be overly afraid of clogging the airbrush but at the first sign of trouble completely remove the needle and flush the airbrush through with an appropriate thinner.
As for number of coats, I found the best way to go was ultrathin dusting coats, such that it needed several passes to lay down even a complete - yet alone opaque - layer. This is where the more basic single action models have an edge because you can set them for next to no paint and it won't move from that.
I mostly used water based acrylics and found they would be touch dry on plastic within a minute and overcoatable in ten - the coats would simply be that thin. The resulting finish was surprisingly robust given how thin it was, but again, that was about colour only rather than a protective finish.
30 year airbrush and larger spray painting dude here << Single cream consistancy, yes to dusting coats, perpendicular to each previous pass whenever possible.
Double action brushes do have thier place but generally it's for more advanced spraying techniques like feathering which is basically a dusting pass but with less paint released - double action brushes are generally used more in the art world and customs spray painting of larger items with artwork like vehicles etc where the scale of the feathering will be less impactful.
Kitty, I would recommend you follow some YT tutorials on learning how to use your spraygun, you can use pretty much any paint, but
acrylic based behaves better than oils as it dries that much faster so you can get more layers and are less tempted to spray heavier if you used oil.
Overcoming the temptation to lay on heavier coats will be hard, but with practice you'll see it's absolutely not necessary and has a LOT of downsides.
Practice, practice, practice swirly shapes, lines, dots - big and smaller etc until it no longer feels "unnatural" to hold but as easy as a pen.
Product called Floetrol - buy some, just do it - will help IMMENSELY with the levelling and application properties and just make the paint behave even better than if it was thinned with water alone.
This is bascially a "hack" to help the paint get to similar behavioral properties as specific airbrush paint like Vallejo which is a "direct to cup" paint, no thinning or anything else required - but boy is it spendy! SO I do this and buy cheaper arcylic paint from art / craft shops which usually still have a HUGE range of colours but need a little attention to get them spray ready.
Old school version of this was to add a drop of washing up liquid to break the tension of the paint, but floetrol does this better and doesn't affect the adhesive properties the way WUL does.
For spraying clear lacquer / varnish, get yourself one of those spotlights with a bendy neck, not anglepoise - no good as you'll need to change the angle as you spray or get yourself a lazy susan - but having both is better.
For your models you can knock up a cradle to hold it with pins - some adjustable versions are available but a homemade one with kebab skewers and that flower attanging green stuff works great - the reason for the skewers is minimal points of contact like those triangular paint stands. Imagine those pin art things a bit like that but with less skewers spaced further apart - will hold basically ANY shape according to how you adust the skewers. - you make it by simply pushing the skewers through to an even height of your choosing, then cut off the rest. Now back out the bottoms of the skewers to about half the depth of the green block - so get a pretty thick one, and cut the skewers again making sure they are still all flat. Now you've got an adjustable throw on the skewers of half the depth of the block.
Only use as few as you can get away with, as it will leave tiny dots with each coat, so you spray, move those and add different ones, spray, move & spray, move & spray - so each pass you're going over the previous dot areas - hope that makes sense.
Just had a thought which is if you're using a stand - do the final couple of coats using the stand glued into the model and "twirl" it in your fingers while spraying the underside, again light passes.
Best spraypainting hack ever.
Do this for a while, then buy a better brush - DeVilbiss, Paasche (spendy), Iwata are all tried and tested brands used by professionals.
Oh and I prefer a side feed cup to a cup fixed to the body on the top, this allows you to get better angles of attack as the cup can rotate 360 deg, very handy!
Oh (again) - PROPERLY CLEAN YOUR AIRBRUSH EVERY SINGLE TIME - I MEAN IT - a gunked up airbrush is good to no-one and significantly harder to clean out.
After shooting paint I generally blow through some water a couple of cups, then half fill the cup with Kitchen degreaser - cillit bang, orange oil something that's designed for heavy duty grease cutting, this will eat through residual acrylic paint aggresively - spray it in then shake it about a bit, shoot this then do that again, but before shooting it, backwash it - which is spraying while having your finger over the needle - akin to gargling if you will, this will agitate what's in the body between cup and needle, if you have an open cup you'll get some spatter so do it over some kitchen cloths, old towel etc- shoot that and do it again, then fll again and let it sit for a bit, shoot again then rinse a couple times with water.
Every few times you've sprayed, disassemble the gun entirely and soak in degreaser for a while, then rinse and reassemble, paying particular attention to the needle.
Sounds like a lot but hardly takes any time at all, you can buy a special spray jar designed to shoot all these dregs into rather than into the air or a sink, but that's your choice.
With a bit of practice you could quite easily add some basic markings to your models, even camoflage with the wood as the base.
Google Alclad - you'll want to try this. Trust me, but make sure your prep work on the model is FLAWLESS or it'll look rubbish.
