FCD is a great tip.
I don't bell the necks on the 357 Sig and have done fine through quite a few loads.
For carry, I load the 124 Speer Gold Dot with AA 9 (around 13 gr) CCI primers.
I also sort by headstamp. Ensures some consistency at least.
Just for messing around, most of the 124 gr bullets either HP or flat point work ok.
I had an 800x load for the Sig but can't really recommend it as that powder is a little touchy due to bulk.
As mentioned before Longshot is good but AA 9 will give you the speed if that's what you want.