Some sort of cleaner, and some airbrush lubricant.
Airbrush paints or suitable thinner/medium for and existing paint collection.
Maybe a airbrush cleaning pot for shooting cleaner into when rinsing out. - not essential but sure is handy.
Also not essential but an inline moisture trap is handy; even thought he compressor has one, as the motor runs longer it gets hot and condenses moisture from the air it is compressing. Keeping ontop of draining the tank and the moisture trap is enough but personally I still use a 2nd inline trap, I find it really helps a lot for fine detail freehand airbrushing, not much of an issue for painting models I guess.
dropper bottles to store premixed paint?
Life time supply of paper towels
Edit; also i noticed that hose wont fit. The compressor has a 1/8inch output. and the airbrush as a badger (only badger airbrushes use this one i think) input.
You 'can' get adapter to go from badger to 1/8inch so that a cheapy regular 1/8 to 1/8 hose will fit.
With what you have picked out your going to end up needing an adapter to go from the 1/8inch male output on the compressor and turn it into a 1/4inch male in order for the hoses 1/4inch female end to fit it.