I'm sure some other more experienced guys will chime in after me, but what I have been told is to shave to 4/32nd. It actually allows the tire to perform better. By the time you run a full tread tire down to those shallow tread depths, you've already lost most of the performance of the tire. By shaving the tire down, you reduce what I call tire squirm. This is basically the thickness of the tread flexing as you put a lateral load on the tire. Its kinda like when you push the skin on the back of your hand sideways. Some say these tires are good for 20-25 heat cycles, and others run until corded. But all start out at shaved tread depths that I know. Running full tread depth will also chunk the tread i.e. chip parts of the tread off.
As for a place to purchase tires, I have been recommended to go to treadzone.com. Haven't bought a set from them yet, but they do contingency and seem to have competitive pricing. I don't think we have a series sponsor that supplies tires.