A 416 Rigby is now coming my way from Champlins. I've ordered a box of Hornady ammo for trial, but assuming I keep it I will need to get a supply of brass and start loading. Hornady brass is way much cheaper than Norma, but I don't know what the quality is like. What kind of brass are guys using, and why?

hornady works great

I use Hornady every chance I can... it's great stuff and reasonably priced.

I third the recommendation and use Hornady brass at every opportunity such as these lately:

400/.395 Nitro Express
.395 Ruger Max
.395 Tatanka
500 Mbogo

Peter Cardona of Quality Cartridge will be making 500 Mbogo brass from Hornady .416 Rigby basic/cylindrical.

Then we'll do .395 Tatanka from Hornady basic.
Then we'll do 400/395NE from Hornady basic.
And so on.

The .416 Rigby brass from Hornady makes great .395 Tatanka by neck-down and fire-form. It is nicely annealed from the factory, and my numero uno choice in brass.

The .375 H&H basic brass from Hornady has been great for .375 Weatherby through 470 Capstick.
Never a hiccup.