This is going to vary from gun to gun. Sometimes it won't make any difference, particularly with a gun that doesn't shoot all that well anyway. With other guns, a thousandth of an inch in bullet diameter can make a measurable difference in accuracy and freedom from bore leading.
The advice to try bullets through the chamber throats to check for fit is generally good advice, but there are always exceptions. If a bullet will not pass through a throat without pounding it through, it's too big.
At a minimum, I'd try the largest bullet that will barely slip through the throat with some resistance and then one slightly smaller. This will probably be .358" and .357" or somewhere in between. Load up some ammo and shoot at least several benchrested groups at 25 yards, or even 50 if your eyes and shooting skills are better than average.
You'll quickly find the best bullet diameter for your revolver. Don't waste your time shooting at distances under 25 yards where everything is accurate.
A micrometer is a big help in doing all this. A caliper isn't accurate enough for this sort of precision. I'd get sample of at least several bullets, trying them for chamber throat fit and measuring them. You may be surprised at the real diameter of some bullets.
