Point conceded about the thinner. I though he meant for airbrushing. For brushing, do use the Tamiya thinner.
For airbrushing, I find that thinning 75/25 rubbing alcohol/paint, at about 18 psi, works very well. (As you've probably noticed the Tamiya paint is VERY thick) The highly thinned paint will not splatter, and because of using rubbing alcohol instead of the Tamiya thinner, it dries within a few seconds of hitting the surface, so you can go over the same area with several thin coats without having to stop to let the paint dry, until you reach the desired opacity.
As far as the airbrush question: With a double action brush, you control both air and paint flow with the trigger, while with a single action, you only control the air. On a single action brush, the paint flow is controlled by twisting the nozzle to open or close it. On the double action brush, you pull pack for paint and push down for air, allowing you far more control. On internal mix airbrushes, air flows around the paint nozzle, atomizing it internally and sending it out the tip. External mix brushes are almost always single action, and consist of two seperate tips, one for paint (coming up from the paint jar) and one for air (coming out of the airbrush) The paint tip is positioned at an angle between 15 and 60 degrees below the airbrush body, and the air tip blows across the paint tip, atomizing the paint outside the airbrush nozzle.
While modelers disagree over which is better for a beginning airbrush, most professional airbrush artists and teachers (the guys from airbrush.com for one) recomend starting with a double-action airbrush. When learning to airbrush, easiest might seem best, but it's not.
The Paasche H is a single action, external mix airbrush:
It is the entry-level airbrush, and works fairly well for basic modeling applications, although you will be able to get a finer spray pattern out of an internal mix brush like the Badger 200:
If you decide to go with a more-expensive double action, the Badger 100 series is the best for the price, although Iwata is quite good if you have money to spend. The Badger 100 series is a top-feed airbrush, which in my experience works better when using acrylics than a siphon or bottom feed airbrush. If you want the freedom of both top, side, and bottom feed, the Badger 360 is the way to go. The airbrush head rotates, so you can attach a paint cup in a top or side position, or a jar for bottom feed.
I would recommend at least an internal mix single action brush - they are far more convenient and are less unpredictable than external mix brushes. If you do decide on a double-action airbrush, both Badger and Paasche have some excellent models to choose from.