I managed to do the entire thing in a couple of hours.
Some pointers:
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Metal Plates. You'll need a lot of them so mine a bunch of ferrite dust if you want to speed up some of the base building, specifically for the power grid & mining.
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Chromatic Ore. Used in just about everything. Find a copper vein after you get the terrain tool, set the tool to it's smallest setting, and mine the entire vein. You'll have just about all of the Chromatic Ore you need after processing it in a refiner. If you dig a tunnel underneath the vein, you'll also avoid the weather.
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Finding water is your best bet for the crystals you need to fix the ship. Floating crystal formations also carry them on occasion, I believe.
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Take a look at the other tiers of tasks, doing them out of order is sometimes preferable. One of them grants the magna-gold recipe for another part of the ship repair.
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If you have trouble finding Larval Cores, look for distress signals from planetary charts, there's a <20% chance that they'll point you to the abandoned building that's surrounded by the eggs.
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you can build a tiny base using the 1/2 size pieces to complete the base building. They cost 1/2 as much so you need less ferrite dust.
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build the minotaur as soon as you can (via the expedition task that grants you the recipe). It can keep you safe from the weather and the hostile creatures. Plus, it'll drastically cut down on on-foot travel time until you get your ship fixed.
Hope this helps!