Even though everything you read about the 357 Sig says the round headspaces on the case mouth, it actually has two datum points, the case mouth and the shoulder. If you search through the posts concerning loading this round, you'll find a recurring question concerning rounds that won't chamber after being fully sized.
I found this out about 15,000 rounds ago, when I first started loading 357 Sig several years ago. None of my shell holders that would accept the 357 Sig/.40 S&W/10mm (5 of them) would allow the case to enter the sizing die far enough to set the shoulder back enough to allow the rounds to chamber in either of my 357 Sig handguns. I solved the problem by milling off several thousandths from the top of one of my shell holders and dedicating it solely to 357 Sig loading. This solved the problem and I've given this advice to numerous people since then, and it's helped them solve their chambering issues.
For bullets, I use Speer 124 Grain Gold Dot 357 Sig bullets, Hornady 124 grain XTP, Berry's 124 grain plated FP and HP bullets, and the Berry's 115 grain FP bullet. I've run several thousand RN bullets through my .38 Swaging die and made them flat points, and then add a cannelure with the C-H cannelure tool. These also work well in the 357 Sig round.
Hope this helps.
Fred