[Adam Skelding]

Most greases used in RC will be fine. The TD 'green' grease, AE black grease or Xray's black grease.

I shim all my diffs with 1 silver shim on the case and either 1 or 0 brass shims on the gear. Best thing is to check that the diff assembly spins freely without the input shaft in place and there is little or no side to side play of the assembly in the case.
Also, check the input gear has little or no end float forward and back with the 'drive shaft collar' #310116 in place. Once all the case is together, check again for nice free spinning and no tight spots.

Like others have said, a couple of runs and the gears 'bed' themselves in. For quiet running the machined gears do offer a big improvement and don't wear out. I've had mine in for over 2 years now and they are still fine.