MY very first rifle, a 351 Self Loader. As a kid, I thought it kicked like a mule. You'll find Hawk to probably be the only maker of bullets. You can buy a swage and turn 357 bullets into fodder but it's hardly worth the time. Assuming you have the correct brass and not brass made from 357 Maximum or 357 Mag, the following comes from an old Lyman manual. Their accuracy load is a max load of IMR4227 under a 180gr bullet. Max accepted pressure is 39,000PSI.
For the 180 Jacketed bullets:
19.0 grs 2400 max load -1800'ps
19.5 grs IMR4227 max load- 1750'ps
For the 200 gr bullets
15.2 grs Unique max load- 1800'ps
18.0 grs H110 max load- 1660'ps
As with any of the old timers, max loads will probably shoot the best accuracy wise but may be a little much for the old iron. Start low and work up. The factory specs per an old Western Ammunition's catalog says a 180gr bullet at 1850'ps was the normal loading. Noting that the max pressure is fairly low, make sure to check the head for any expansion for excessive pressure as it probably is not going to show up on the primer.