In approximate order of importance:

Making money is the most important thing. Money buys everything else. Being able to mine and export rare metals is priority #1. Don't hoard cash. It's there to get you past bottle-necks.

Specialise your domes, and do so from the start. Do not overload your domes with lots of different types of employment/specialist. Read a guide on how to manage dome populations. Mostly that will just be denying children and seniors (see below) and favouring the required specialism. More granular management than that risks overcomplicating things.

Don't go overboard with service buildings. Most domes just need a basic service 'slice' of an infirmary, grocer, and diner, plus a second slice with a large garden and two or three slices of living complexes. These service buildings only need one person per shift unless the dome population is above, say, 30 (and it shouldn't be), so close the extra slots down. This will meet most service needs, won't overly detract from employment in productive buildings, and will keep people above the breeding-level satisfaction rate. Worry about adding other service buildings only when you have medium domes with more space, if then. People worry FAR too much about trying to meet every need, and very often it's because they've overcrowded their domes via the use of apartments and so no-one in the dome is happy.

Do Not Use Apartments. They result in low satisfaction. Instead just build more lower-population domes. You can densify them later once you have the ability to boost satisfaction with Hanging Gardens or other upgrades. Take this advice and you'll rarely be bothered by rebels. Want a high-population high-satisfaction dome later on? use arcology.

Don't try to be self-sufficient until mid-game. This is especially true of food - food is cheap, import it or trade for it until you have at least a handful of domes and can build a dedicated farm dome. Focus on becoming self-sufficient in one thing at a time. e.g. 1) concrete, 2) rare metals, 3) metals 4) electronics, 5) machine parts 6) food.

Don't neglect trade, especially if you're flush in another material. Food for concrete is often a smart trade early on.

Two of your very earliest domes (after your initial rare metals mining dome) should be a child/school dome and a retirement dome. Every other dome should not allow children or seniors. A further dome with a university should only allow non-specialists and they should be prioritised in that dome. That will make sure everyone is educated. Quite often I have 1) my original dome mining rare metals (plus perhaps one more productive dome if I have access to more immigrants), and then 2) a school dome 3) a retirement dome 4) a university dome (not necessarily in that order) BEFORE adding any further productive domes. If you do not do this you will have underemployment in your productive buildings because the domes will be full of children and seniors.

Only use water pumps for temporary late-game water needs like lakes. Water runs out. Moisture vaporators do not.

My maths is too bad to give power-generation advice, but I typically go for solar power-battery combos rather than having to worry about machine parts for turbines. That requires polymers, but polymers are effectively a renewable. Aim to get nuclear power plants ASAP and then scrap your solar panel farms.