Couple of notes for Paasche airbrushes.
1) They are air hogs, they really do use a lot of air (about 1.5x to 2x as much cfm as an iwata hp-cs, for example) So make sure you have a compressor capable of keeping up. The hose acts like a buffer/tank so you shouldn't get to much 'pulsing' so long as your hose is long enough and the tank can keep up. (different than the sputtering Josh was dealing with)
2) The Needle, valve, and cap are a matched set, and don't work so well when switched around. The cap and needle are usually pretty easy to identify as they should have rings cut into them to represent their size, 1, 3 and 5 rings respectively. The valve is more difficult, but if you put all three together you should be able to tell which is which by putting them in order based on the size of the holes. Once you know which is which, use a fine tipped permanent marker and write the number on the outside of the valve.
3) Sputterring can be caused by a couple things, but usually it is caused by the parts in the trigger and air valve section. In the diagram this includes parts 7, 23, 24, 25 and 26. When you press the trigger (7), it pushes the plunger/needle (24) down compressing the valve spring (25) and allowing air to pass through the valve nut (26) past the punger (24) and oring (23), into the head of the brush. The most common cause for sputtering I have seen is some kind of restriction preventing the valve from opening far enough. This can be simple stuff like the valve nut (26) being screwed in too far or crossthreaded, or something like a tiny burr/debris preventing smooth travel of the air valve mechanism. The trigger should depress a good 1/8 to 1/4 inch when pressed, if it does not move very much (less than an 1/8th) you may need to adjust or reassemble the valve mechanism. Another cause is a faulty/swollen/damaged oring. A cheap solution for this is to go to a dart shop and buy orings they put on the flight shaft of darts to prevent the flight shaft from loosening from the body of the dart. I bought 50 of these orings for about $4 USD. Important note: If you get bubbles in the cup/resevoir when the sputtering occurs, but not when the sputtering is absent, then the problem is more likely some kind of blockage in the head of the brush, which can be anything from a peice of dried paint moving around, to a damaged tip/needle. If you get no bubbles when it sputters, definitely check the air valve section.
It sounds like you've got this problem mostly sorted, but Ill leave this here in the hope that it helps if someone else has a similar problem in the future.