Your four priorities are spot on. You can also think of 2-4 as:
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Acquire resource (Economy)
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Stop your opponent from acquiring resource (Aggression)
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Stop your opponent from stopping you from acquiring resource (Defense)
Those three different play-styles make up the crux of the strategic game, and share an RPS relationship between the three of them: defense > aggression > economy > defense.
The first priority you listed,
Intel, has an interesting unique relationship with the others. Instead of directly taking part in the RPS of the other three, it serves to help you decide which of side the triangle to focus your play-style on. I.E., see a porc fortress and counter with fast expansion. (Also from a lower-level more detailed perspective, you can use it to determine your unit composition to counter your opponents play)
What is also interesting about intel is that, while investments in eco, aggro, and defense are pretty distinct, intel is often the second purpose of raiding or attacking.
So I agree with you, as a general rule you want to start the game with an aggressive mentality, and then be flexable with your playstyle as you get intel.
