how to choose layer stack?
You use the 'right' layer stack for your application. That is, you let the application decide.

FR4 is the default material. It's cheap, everyone uses it. So do you.

Single layer is the cheapest, with 1/2 oz copper. Thick enough for strength, but thinnest is cheapest. 0.8mm is OK for small boards, 1.6 usual for larger ones.

Can you use single layer 1/2oz 0.8mm FR4 in your application? Yes, done.

No? Need a ground layer, or another routing layer? Double sided is not much more expensive than single, and is probably the default for the majority of PCB designs. If your project can't use this construction, you have some significant constraints.

Need it more compact, so need additional layers with vias for routing? Need additional ground layers? Think you need a power layer - you probably don't - it's a bit of a double-edged sword, avoid if possible. Need thicker copper for the current?

Need low loss at microwave frequencies? Then you can't use FR4, try RO4350. But, you'd be surprised how high frequencies do get pushed across FR4 boards, especially if they're small where loss is less significant, it gets used in 2.4 and 5GHz+ routers!

Whatever you end up with for the stack, choose one of your supplier's standard ones, that they have a stock of materials in for. A really good recipe for delays, errors, and rapidly ballooning expense is to get a PCB supplier to do a non-standard build that they've not done before. If they say they do it, but don't have stock, it should ring warning bells in your head.