My process at the end of the day is the same as Big john above, with the addition of blowing a cup of cleaner through when the needle is out, just be careful of the angle you are holding the brush or you'll wind up with cleaner flowing back where its not needed.
Given that you asked what cleaner rather than how do we clean the brush, all of the above are used by many of us, just be careful spraying the isopropyl in the air, a spray out pot is strongly recommended, not great for you lungs, !
I use what i have on hand, it can be a comibination of
windex
water
isopropyl
Createx reducer
Createx airbrush cleaner
After you've dumped the excess paint, another great method that works great with side brushes and the A or B size cups is a mug of warm water with a drop or two of dish liquid in it. submerge the front of the airbrush so the cup is submerged, wind up the PSI then just use the trigger like you would when you are painting, and let it all cycle through, rinse out using water/reducer.
This will also work with C size cups but you'll need a deep mug as the brush needs to go in almost dead vertical, whereas the other sizes can be angled.
Immediately dump the content of the mug unless its plainly clear that it is not your normal tea or coffee mug, i'd hate to think someone picks it up and takes a big swig