I reload a lot of 357 cases, all to target velocities. I use once-fired as well as new brass. New is Starline or Winchester. They are reasonably priced and last several loadings. I avoid the so-called premium brass. The manufacturers are so proud and charge a premium price for lower quality brass.
I recently did a study on rifle brass to see if the prices on the premium brass was justified. I used 308, loaded again to target velocities. All was new brass by Starline, Winchester, Peterson and LaPua. The Winchester and Starline loaded flawlessly. The premium started with issues having the cases leaning off to the side, the bases and case not in alignment, difficult sizing, some not even wanting to go into the sizer die and cases so poorly made that they collapsed the shoulder when loading premium match bullets. The premium brass never made it beyond 3 loadings without a failure, The Starline and Winchester went on for several more loadings. You don't always get what you pay for.
In the photo, left to right, Collapsed shoulder, normal cartridge, crooked cartridge.