That depends on which version you bought: fine, medium or coarse (AKA large). Chances are it's the medium needle, as it's the most popular. The Pro set comes with all three. One way to tell is to unscrew the handle and examine the non-pointy end. Two minute grooves is the "medium", one is the "fine" and three is the "coarse". When I say minute I mean it. I couldn't remember which was which and had to use a magnifying glass to see them! "What a drag it is getting old"!
Fine is really only suitable for inks or extremely thin paints, the coarse is designed for textile paints. Medium is used for pretty well everything else. You need to match the head assembly with the proper needle for the airbrush to work properly.
The color cup is for when you are only using a small amount of paint. It wastes less paint than using a bottle. I also find that since it has a shorter "draw" you can use a slighty lower air pressure to use it.
I have multiple color cups and swap them out when changing colors rather than spending time cleaning them. I keep an old yogurt container with Windex in it and just drop the "old" cup into it for a good soak while I continue painting.