Is there an ideal way to centering these things?
The very first I do with a new sprocket is see if it is true on a flat surface, or warped to begin with.
A warped sprocket will never be true which is what leads to chain jump problems, it's not uncommon, I must have 40 warped sprockets on my shelf.
That looks like a coaster brake wheel.
Make sure there is no dist cover in the way and the sprocket can fit over the hub.
Now eye up your rear sprocket chain line to the engines sprocket to see if you need to cup it in or out.
It really bites if get this wrong and have to flip it.
Sandwich it up, then get all the nuts firm and centered the best you can by eye.
Start with bolts through where the inside plate pieces meet.
You want them to form a perfect circle, not overlapping or offset.
I like a deep 10mm socket and my hand drill to get everything firm but movable.
Next you are going to need a truing stand that will hold the wheel and allow it to spin.
For me that is just a front fork upside down in my bench vice.
Mount your wheel in the stand and give it a spin.
Look directly at the sprocket face and see if goes up and down by just focusing on something through the spokes, like a spot on the wall, and you can see it.
If you can see it going up and down catch it the highest point at the top.
Now get yourself a short piece of chain and lay it in the teeth at the top.
Get yourself a hammer and tap the sprocket down just a little.
Take off the chain and give it another spin.
Repeat until it is true as that is what causes chains to get loose, then tight, then loose...
Now to tighten it up while you get any wooble out...
Look from the edge of the sprocket for back and forth wobble.
Start tightening up the nuts where it wobbles to the outside to pull it in.
This takes awhile with lots of spins but that is what causes chain jumps.
Hope that helps ;-}