I use the branded thinner for actually thinning the paint, whether it be Scalecoat II or Floquil or Model Master paint. For cleaning up, which uses a great deal more solvent, I break out the jug of lacquer thinner.
One reason for not using craft paints through an airbrush is the pigments aren't ground as finely as a more expensive "artist" or model paint. There are more imperfections in the quality and consistency of the pigments, which makes their cost lower, but increases your chances of finding a chunk. It's not impossible to clean chunks out of a tip, but if you start out with a fine spray pattern tip, you may end up with a wide spray pattern airbrush!
If I'm not spraying with Scalecoat II, Model Master or Floquil, I'm using artist's oils. They come in tubes and are easily thinned in small disposable mixing cups (about the size of a Nyquil dosage cap) with turpentine. These paints are great for weathering because they can go on in such thin coats, they take a long time to dry which gives you time to work the finish and the colors you can mix with them are virtually infinite. Back in college I used to paint landscapes using an airbrush and oils and the results are quite nice. Incidentally, the diorama in my avatar image was painted with oils over Sculptamold hills, even though you can't really see it well in that tiny picture.
You don't need an expensive airbrush to paint. I got my Paasche model H for $45 several years ago and I bought one for my brother on ebay recently for $30. I picked up my compressor at Wal-Mart for just under $100 and it does the job nicely. I use that compressor for other jobs around the house, like inflating rafts for the pool or filling up low tires, etc. so I've been able to justify the expense.
On top of that, the compressor was cheaper than my old "airbrush" compressor that didn't have a tank, was noisy, and could be counted on to "spit" water through the line in a matter of minutes.