Those targets look pretty darn good to me, especially with a new-to-you handgun.
I've shot Gold Dots and (many years ago) Black Hills loads through various .357s with no problems. My preferred load over the last few decades has been the old Federal Classic .357 125 grain JHP load. Nothing fancy, but it was easy to find and relatively inexpensive, so I could afford to shoot some on a regular basis to stay in practice.
Personally, I'd feel well-armed with any modern non-trick-bullet, light-to-medium-weight .357 load nowadays, and I'd let availability and point-of-impact in my fixed-sight gun be the deciding factors in choosing between them.
Enjoy that new blaster!
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)