What is the best strategy when it comes to occupation?
Civilian government, or Local police, etc.?
Should I worry about uprisings, revolts, etc.?
I don't understand the mechanic, what is the best strategy to handle it?
The answer isn't so quick but will try to keep it as quick as possible without just saying: "It depends on your goals"
Shortest answer:
If you don't want to deal with it all the time and looking for a quick fix: "Usually", local police force is a safe bet.
"Usually" keeping resistance below 25% for every state is desirable. So get whichever does that if there is high resistance.
You want resources now: Forced labour
You want factories now: Harsh quotas
Long answer:
There's no best strategy for everyone, every approach involves different benefits & hindrances - over time & immediate.
Laws with more compliance growth are usually a more long term thing and you want to be committing to keep the state under your control and to benefit more from it long term, by paying a price in losing more garrisons (men & equipment) & risking sabotages more short term.
Scenario 1:
You captured some states with a lot of aluminum, and you were importing a lot of it to produce planes.
Suppose that forced labour occupation law on that state means 5 civilian factories saved for you at this point and you think that's a good trade: Go for it.
Later, you got more aluminum from other places and you're at a surplus: Lower down the harshness and go for other laws now.
Scenario 2:
You captured a state with no factories or resources, but with good population, so you can get manpower from there.
You have enough manpower and spare rifles for now, but may need more manpower long term.
Looks like you also can stay below 25% resistance with the best compliance law: Go for a more compliance oriented law.
Thresholds:
One thing to watch out for is that there are certain thresholds at state level for resistance, which are nasty.
So make your decisions knowing where you will end up between those thresholds. 25% resistance is one.
There are also some at country level for compliance.
If you're close enough to them, you may want to achieve a threshold first before going for the law you want long term.
I really like the mechanic and would advise people to read that tab in its entirety and fiddle around with it and discover more of its quirks.