Well, the general advice is to slug you barrel & load your slugs .001" to .002" over your slugged bore diameter. Also, don't try to push a plain based bullet past it's hardness range. Mostly, the harder your lead alloy, the faster you can push it. If you want to hunt with it, go to a gas check bullet if you want soft lead (to expand) at faster velocity.
For best accuracy, the bullet needs to fit the throat (diameter and cartridge OAL).
With the Handi 357 mag, a chamber cast could be real helpful, many are chambered (and throated) long. My Handi could chamber a 360 Dan Wesson case with no problem & still had .020" to go. The throat on the other hand, was cut long enough to let a .357 Max length round load. So there was quite a bit of bullet jump.
I got real good accuracy with 200gr RCBS & Saeco designs in 360 Dan Wesson cases seated to 357 max OALs. Most of the 38s & 357s were ok plinking accuracy, but nothing great.
I've since reamed mine to 357 Max, but haven't really tested enough to see what it will do yet.
Hope that helps.