I'm not an expert but have spent some time airbrushing (got something arriving today hopefully to assist with it
), and I would recommend, given my own limited experience.
A Harder & Steinbeck brush, they start at around £50 (for an Ultra) which is a lot more than some brands, but you'll be able to get spares very easily (we have an Ultra and a Evolution Silverline 2 in 1 FPS*).
For a starter brush the Ultra is nicely made, spares are readily available (it shares a lot of the internal spares with other H&S brushes), and it's pretty simple.
We use a compressor with a 2.5l tank, I can't think off the top of my head what the brand is (I think it's Sparmax, or an unbranded Sparmax), but you can get cheap compressors from about £50 on ebay, but the build quality on unbranded chinese imports varies massively.
Normally if you buy a compressor you will get to choose between models with a tank and without, go for one with a tank, it means the motor won't have to run all the time (which is better for the motor), you won't get as many pressure variations, and it's generally worth the little bit extra.
Do NOT get a garage compressor (the sort that has a 25l tank), as they are extremely noisy, although there are some that are designed to be quiet/silent, but they tend to cost a lot (almost all airbrush compressors are "silent" as they're often intended for use in classrooms, art studios, or nail salons).
One thing to note is that you can get quick fit couplings for airbrushes and compressors, get them if your brush and compressor don't come with them already, it saves a lot of mucking around when you clean the brush, or want to change brushes (if you end up with more than one).
Re paints, Vallejo do some pretty awesome airbrush paints in their Model Air range (including about 16 colours of airbrush undercoat which are far cheaper than spray cans, about £10 for 200ml but that is all paint), and now a new Game Air range which I'm eagerly looking forward to trying out - I've got about 6 bottles of the two colours I use for my Tau on order.
Vallejo do a paint thinner (the new clear one) which is pretty awesome and about £6 for 200ml from memory, it seems to work at about 1:1 with Citadel layer paints to thin them down (assuming you've not got a bad pot of citadel paint which we seem to keep getting).
Other things you'll probably need.
Airbrush cleaner, you can get both a bottle of stuff you mix with water and run through for general cleaning, and a "liquid reamer" which is much harsher and in spray cans like WD40 (make sure it has the straw with it).
Cotton buds.
Kitchen roll or strong tissues (to help clean the needles).
A few cheap beakers or cups to hold water so you can pour it into the brush and flush it out quickly.
Something shallow and reasonably heavy to sit the nozzle and end cap in to soak if needed (it only needs to be about half an inch deep).
A magnifyer of some sort - you will almost certainly need one to assist in spotting specks of paint in the nozzle, you can buy a 30x jewelers loop type thing for about a fiver of less from Amazon etc.
Good lighting.
Some form of turntable, I use a mixture of cake stands from Aldi's (large surface, cheap), and Tamiya stands (smaller, designed for model work, but about £20 for a pair).
Some form of stand or holder for the brush, until I bought a proper one I used a hook intended for holding things like spades in the shed (99p store and wilkos do them packs of 4-6),.
Something to rest the needle on when you're cleaning the brush, so that it won't roll away or get knocked about, I cut a long shallow V into some of the sort of foam that graphics cards and Antec cases tend to be packed in.
I would also strongly recommend getting a face mask as whilst acrylics aren't as bad as enamels for spraying, if you're going to do a lot it is worth the cost (I use a mask that cost about £15 and the filters are about £15 every couple of years).
As an example of what you can do with very little practice with an airbrush I did these Tau hulls as pretty much my first attempt to use the brush properly a couple of years back.
It took far longer to cut out the camo mask and apply it than to do the 3 or 4 coats of actual paint (two coats of each colour).
*The Evolution brushes start at around £80 and are highly customisable, for example the 2 in 1 comes with a pair of needle/nozzle combo's and a pair of paint cups, and almost all of the Evo brushes let you add options later (for example you can choose up to about 3 different needle sizes, paint cups from 0.5ml to 50ml.
