I use an airbrush to paint my foam puppets, I just bought a starter kit at Christmas Tree Shops. The brand is Badger, as for the model I would have to look. It was the cheapest one there though. I would suggest starting out with a cheap model and playing around a bit before looking at a fancier 'brush. They are a lot of fun and quite easy to get the hang of. My suggestion is to start cheap, play around and go from there.
I painted tees and such in malls for years here in Memphis. I started off with a single action Binks Wren, but quickly bought a Paasche VL dual-action brush and have stayed with them ever since. They're not too expensive, and can do fine lines, or bigger spray areas. I've shot acrylics, house paint, liquid make-up, and more thru the one's I've had over the years. You can find them (and replacement parts- very important for airbrushes) at most art and hobby shops. Createx paints are good to use for a lot of different uses.
One thing most people don't do is get a decent compressor. Get one with a holding / resevoir tank. They can be the small 'pancake' kind, or the bigger belt driven ones, and are not that expensive if you shop around.
There're also some magazines out there such as Airbrush Action Magazine that can give you some good advice and tutorials.