First generation Ryzen struggles with higher memory speed. You very likely will not get the full 3600MT/s. There’s no real reason to buy slower, just be aware you’re likely going to hit a ceiling.
For gaming you might see bigger improvements from upgrading the CPU, maybe to an R5 3600. That and the memory are both going to offer big performance improvement.
Some B350m models did get Zen 3 compatibility. Not all, if I remember correctly, though I could be wrong. So whether it’s compatible I think is model dependent. Whether an old B350m has the VRMs for a chunkier CPU would also be a reasonable question.
I mentioned the R5 3600 because the prices on them are great. A 5800X3D does perform better, but I see completed eBay listings at $225+. They also needs a cooler. I see one 3600 that went for about $50 and several that went for $60, which isn’t too much more than a 16gb kit of DDR4.
I would definitely consider a Zen3 CPU for this upgrade, depending on budget.