The .357 is well known as a bear for leading. In general, the best solution is to use a gas checked bullet, as some guns refuse to shoot plain base no matter what tricks are used.
Beyond that, a few general principles:
.357 Magnums in particular want a good relationship between throats and bore. Ideally, throats will be a thousandth over groove diameter, which in the Magnum generally means grooves of .357" and throats of .358". If your throats are more than a few thousandths oversize, or -- and this is bad -- even a slight bit undersized, leading will result. If you can accurately measure both throats and bore, you can rule out -- or in --a major cause of trouble. At the least, it is a good idea to slug the bore and then attempt to pass the slug through the throats. If it doesn't fit, you have a real problem, and have no choice but to open up the throats if you want to use cast bullets. If the bullets pass through the throats with mild pressure, you're good, and if they fall through without any effort at all, you will probably have better results by using bullets a few thousandths larger than your current batch.
The bore itself is also quite critical. It needs to be pretty smooth for good success with cast bullets, and it really helps if the bore tapers from breech to muzzle. The most common issue here is choke at the breech where the barrel screws into the frame. This often results in a constriction, which in turn sizes down the bullet and then releases it into a now-oversized bore. Vicious leading can result. The cure is fire-lapping, which can almost be magic.
As far as bullet hardness, IMO it's not as important as some believe. A very soft bullet obviously does not belong in the .357 Magnum, but good results can be had from as soft as 12-15 BHN -- much softer than most factory hardcast bullets. Of course, a bullet that soft really needs perfect gun conditions, but by the time we get to 16+ BHN -- still much softer than most commercial bullets -- additional hardness isn't of much help, again IMO.
I do agree that bevel bases make life much more difficult, and should probably be avoided where possible.
And I also agree that lube can play a critical role. IMO most factory bullets come with hard lubes which are not ideal, especially in the .357 Magnum. I've had good luck with several commercially available lubes, but commercial bullets are a mixed bag, in my experience. I strongly disagree with the suggestion of Lee Alox. I have had uniformly terrible results with any sort of tumble lubing, and I know from conversations with others that I am not alone. Doubtless there is somebody out there who can drive tumble lubed cast bullets to top velocity without problems, but I don't know him. I think you're putting yourself behind the eight ball with it.
And here you thought it would be easy!
Short version: Slug your barrel and throats and use bullets that fit. Gas checks make life a lot easier. And if all else fails, even an idiot can get decent results from jacketed slugs in the .357 Magnum.
Have fun!
