Anybody care to recommend what brand of brass to buy?
Should I spring for the Norma brass or try another brand?
New to this caliber. Thought I'd have some fun.

Well - I just use the cheap W-W bulk brass from Midway USA. They have been plenty consistent and the brass longivity has been fine. IMO, it's not worth spending the extra money for the Norma brass.

For my 7x57 I use Norma brass. I got it because the Winchester that I ordered was out of stock. I'm glad I got it;the stuff requires next to nothing to prep. The flash holes are drilled and require no uniforming and the primer pockets don't need any work either.

I have been loading the 7X57mm now since 1972. Most of my ammo is loaded in Remington brass, some in Norma, and maybe 20 or so rounds in WW cases. The Norma brass, while excellent, is not enough better than Remington to justify the additional cost. Remington 7X57mm brass lasts as long as Norma. The last 100 rounds I loaded are in Remington nickle cases. Unfortunately, Remington recently discontinued nickle 7X57mm brass. This group, and a lot of similar ones, was shot with Remington cases and Nosler Partiton 140-grain bullets, from a Ruger M 77, no less.

I've used quite a bit of excellent Norma brass. However, I've had quite a bit of trouble with Norma brass lately - split case necks mostly, after only a few reloadings and at moderate pressures. Had some overly deep primer pockets on some other cases (in other calibers) as well.

I have used Fed cases and WW in 7x57, both have been much better than the recent lots of Norma.

Remington or Winchester ... whichever you can get the cheapest.

Rem or Win. IMO the Norma is definitly NOT worth the extra cost.