This may not be specific enough for you, but I have shot many different factory 357 and 38 spl as well as handloads..
All have been satisfactorily accurate out of the Handis I have had.
I've always managed to get 1 to 1.5 groups with iron sights at 50 yds. And one gun and barrel combination, scoped and sighted in at 100 yds was a 1.5" group shooter with most ammo. Chances are with a bit more tinkering with loads, I could have had it shooting 1" or less - but I've mostly just used the 38spls in my barrels for plinking.
I'd say just experiment until you find what works best in your gun.
I expect others will respond with more specifics about their own experiences, but I just wanted to give my .02 worth.
Have fun with your new toy. :grin:
Cheers
Kerry