Exactly needed to airbrush;
An Airbrush... you seemed to be aware of what kind is suitable.
A hose to connect it to air supply.
An air supply; Compressor is best, cans of air is worst, car tire can work okay, compressor with tank is best choice but may be out of price range.
A moisture trap, usualy theres one built into compressors, can get inline ones to go between 2 hoses, or ones that connect to base of airbrush, all are good, need atleast 1 (I use 3; one of each) more of them means the air source needs to work harder.
Some paint. Citadels acrylics spray okay when thinned properly, I use Liquitex Airbrush medium to think them, Other choices might be vallejo model air, or badger minitaire for premixed, or any other acrylics and thinner combo.
Some cleaner for the airbrush, Isopropyl alchol or acetone can work well, check out what is safe with your airbrushes seals and coatings. Theres lots of branded cleaners too if your unsure, although you pay for the brand.
Paint mixeing, measuring and storage stuff... cups, pippetes, cocktail sticks etc.
An old brush for cleaning the airbrush with, and maybe some small pipe cleaner things (airbrush sites often do a keyring of these)
Thats all you really need.
Nice extras might be an extractor, a respirator mask (saftey first

), a stand, cleaning pot, quick release couplings for the bits.
A lot of people dont wear a mask, and its 'reasonably safe' ish... some paints are a lot more toxic than others, generally were talking about water based acrylics which arent the worst, but still might aggrovate asthma or other respirator problems, being somewhere well ventilated is often enough at the scale of work we're looking at with mini's.
A good store I find within the
UK is
http://www.everythingairbrush.com/
they stock a fairly wide selection, and spare parts for all the brushes they sell. They might wlel ship world wide, but there is probably someone closer to you if you look around or get a lucky suggestion from a dakkite