Lacking any specific info, 15 PSI should at least be a decent starting point for air pressure. I have a decent variety of airbrushes and all will paint fine at that air pressure. From there experiment with things. Your variables are the air pressure, the paint thinness, distance of the airbrush from the model, and your needle position and any can affect your painting.
For fine lines, lower airpressure will usually better control, but if you lower it too much, the paint will not atomize as well. When you're painting fine lines, you need to get your airbrush tip close to the model, maybe on the order of 1/4" - 1/2" distance.
As for thick paint,its best avoided. If your paint is so thick that you have to crank up the pressure way beyond that, you probably need to thin your paint some more. If your paint is too thick, you won't get nearly as nice a finish as you could with properly thinned paint.
As Jesse said, if you can supply some more specific information, we can give you more informed suggestions.
Andy