Best brand of .357 ammunition?

the best at what?every gun can shoot differently.some bulk ammo is just plain junk.

For factory ammo in a handgun you just need to keep trying stuff until you hit on the one that shoots great. I have a 357 that really shot Federal Classic 180 grain HP's good until it went out of time and was sent to Colt for repairs. When I got it back it wouldn't group them well anymore. I went thru a few selections before I got some Hornady xtp 158 grain HP's and these things are 1 3/4" @ 75 yards with open sights.

Looking for accuracy for close range deer hunting as well as target shooting. Will be shooting a Ruger GP100 6".

For factory loads - I generally stick to Remington, but have had good luck also with Hornady loaded rounds.

My bulk buys are usually Remington UMC or Federal Eagle/Classic

I think the best way is to just buy the 20 round boxes of different brands and weights until you hit on something it likes. Different brands of guns have different twists and even barrel lengths will affect what shoots good and what doesn't. There just isn't anyway to tell until you try it and see how it groups.

If you handload you just do the same thing; keep testing different powders; charge rates, bullet weights and brands etc. until you find something that clicks. I got very lucky with the last brand and weight as I found it in 3 selections. I still want to find a good .38 special load for it yet.

Yea, of you want real good accuracy, you are going to have to try a few & see what works.
However, I have shot the Speer gold dot soft points, 170 gr for deer. They were rather accurate out of an older GP100.

I'm guessing thse are being shot from a Ruger GP100 w/ a 6" barrel. My gun that is that same shoots what ever I shoot out of it the same (I have the same gun). I haven't shot a tone of different loads, but they all seem to shoot about the same. They seem to do their part if I do mine.

If I were shooting factory loads I would choose one that performs on target that like I want, and test a few. I'm sure there will be some that don't shoot worth a darn.

If you are looking for just close range deer hunting I would try a few different 158gr loads. Don't look past the soft points either. They may work just fine. I shot some 158 gr American Eagle soft points out of my gun, and they shot very good. I wouldn't hesitate to shoot a deer with one as reasonable distances.