My son has a Ruger #1 International in 7x57 and we've tried a few things in it. My take on the 7x57 is that it will never be a speed demon, it's not a 7mm Mag. Especially true in the short barrel of the R#1 International.
So, to that end we choose a Hornady ELD-X in 162 grains. The ballistic advantage makes it shoot flat(ish), and the ELD-X is a decent whitetail bullet. My son harvested a eater buck this last season and no complaints on expansion or retained weight.
For hunting, I prefer the newer powders as they are stable, not much temperature variation. To that end, the powder I load with is IMR4451, 46 gr. But I do load longer than the book. My OAL is 3.125 which is still a bit shy of the lands, and it is fully supported in the neck, IIRC. Velocity is around 2550 fps. I measured the PRE and I am near or at MAX. for my rifle. I used Federal brass with a case weight of app 175 grains. Accuracy in R-P brass, 185 gr app, was not as good. Caveat: The bore is somewhat neglected, some pitting but rifling is sharp. This tends to make rifles a bit fussier on loads.
BTW: I bought a Lyman Borecam, it's a real reality check. It's a good idea to clean your rifle bore, minimum a bore snake with some Ballistol. In my son's #1, it takes a few rounds to get the accuracy back after a thorough cleaning.
With lighter bullets I seemed to have decent performance with Varget. Until you get up in bullet weight, powders in the 4350 burn rate are a bit slow for optimum performance.
For cast loads I use a Lyman 287346 GC sized at 285 with SR4759, 20 gr. (a starting load), with decent luck. This load worked well in a somewhat neglected Mauser as well.
As noted above, there are large variations in brass. Weight, internal volume, strength and dimensions. I have some brass that needs a different shellholder.