I got into the shot deal quite a few years back and since I already had several sizes of shot from 9 up through 2 I played with some of it all.
For hte standard loads I found that 7 1/2 worked out the best in the 44 while the 8 worked out best in the 357's. For other kicks and giggles I also loaded up some of the 4 which in the 357 with a felt underwad inserted before the little plastic cap would allow nice groups to a further distance. I too have taken squirrel, rabbit, quail and dove with those so loaded shot rounds. Best shot ever was a cotton tail quick draw which rolled it in mid stride.
Then there was my adventure into bigger shot for the 44 which resulted in these for my 44, they use the Speer #5110-.350" lead round ball,
They are pretty accurate and good for small game out to about 15yds or so.