Great advice so far. Don't even bother with jacketed .357 bullets in your .363 bore--you won't get accuracy, but at the low operating pressures involved, there's a decent chance of getting a bullet stuck in the bore. You'll even find that some makes of 38 S&W brass are suitable for these smaller bullets, but others won't be--you can't get sufficient neck tension to make a consistent cartridge. Lead is the way to go, and Matt can help you greatly if he's caught up on his backlog.

I shoot a number of different revolvers in that caliber, and although it's practical to use 38 SPL component bullets for the .356-.357 Colts and Rugers, and often even in the .359 solid-frame Smith & Wessons, groove sizes of the older guns often are in the .362-.365 range. For these, you'll need to cast them yourself or track down a commercial caster.