I have an AK barrel in the white.  It's going to be used in a build that will get a camouflage paint job.  Nothing fancy, just a spray paint finish.

So, can I finish the barrel with a simple primer/paint combo, or is something more durable needed as a base coat?

When you are done building the rifle and get the barrel populated and installed into the reciever, what I suggest is heating the populated areas with a heat gun and letting any oils leach out. Then let it soak in a container of acetone for awhile. Then blast it and use high temp Barbeque spray paint, the kind you can get at Home Depot. If you do it this way, you'll have a fairly durable finish. There is no priming, instead 100-120 grit aluminum oxide blasting is what you want.