A station is any building that performs a function, except for the spirits' houses and the buildings listed below.
You do not have to improve every station on your boat to accomplish this first part of the quest.
In particular, at least the following stations do not need to be upgraded:

• Gardens
  
• Animal Pens (Sheep/Cow Corrals)
  
• Chicken Coop
  
• Cellar

You need to upgrade:

• Smithy
  
• Crusher
  
• Foundry
  
• Kitchen
  
• Loom
  
• Sawmill
  
• Windmill

These are the ones that I've upgraded and progressed with the quest.

For the blueprints, I'll leave this guide down below; https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=2233491335
Reminder: you don't need to upgrade all stations unless you want to.
If you want to get all the materials to upgrade all the stations at once, here is the list and how to get them.

• 1 Steel Sheet (Requires 1 Iron Ingot and 1 Carbon Powder)
  
• 5 Gold Ingots
  
• 12 XP Potion (Buck's event)
  
• 1 Celestial Sheet (Requires 1 Comet Powder and 1 Pulsar Ingot, Meteor Shower and Pulsar Rays event)
  
• 890 Glim

• 5 Pulsar Ingot (Pulsar Rays event)
  
• 6 Comet Powder (Meteor Shower event)
  
• 6 Carbon Powder (Crush Coal on the Crusher)
  
• 6 Silica Powder (Crush Quartz on the Crusher)
  
• 585 Glim

• 12 Nebula Fabric (Nebula Pillbugs event)
  
• 8 Lightning in a Bottle (Thunderstorm event)
  
• 7 Bright Jelly (Jellyfish event)
  
• 510 Glim

• 5 Bright Jelly (Jellyfish event)
  
• 8 Lightning in a Bottle (Thunderstorm event)
  
• 12 Linen Fabric (Hummingberg sells Linen seeds)
  
• 0 Glim

• 10 Maple Plank (Available in early regions like Barkensheim Creek)
  
• 18 Linen Thread (Hummingberg sells Linen seeds)
  
• 8 Bright Jelly (Jellyfish event)
  
• 120 Glim

• 8 Aluminium Ingot
  
• 18 Maple Plank (Available in early regions like Barkensheim Creek)
  
• 12 Lightning in a Bottle (Thunderstorm event)
  
• 285 Glim

• 6 Bright Jelly (Jellyfish event)
  
• 5 Pulsar Ingot (Pulsar Rays event)
  
• 7 Pine Plank
  
• 840 Glims

Hand over these materials to Francis;

• 7 Citrine
  
• 7 Hematite
  
• 7 Opal
  
• 7 Amethyst
  
• 7 Diamond

If you have the Improved Tools Ability;
Plant Quartz on the Turtle Sisters. Mining them will give you Citrine.
Plant Aluminium on the Turtle Sisters. Mining them will give you Hematite.
Plant Marble on the Turtle Sisters. Mining them will give you Opal.
Plant Limestone on the Turtle Sisters. Mining them will give you Amethyst.
Plant Coal on the Turtle Sisters. Mining them will give you Diamonds.

It's highly recommended that you have this tool. If that's not the case, here's how you can get it;
Complete the Errand "Saturday Night Shopping List" from Francis. To complete it, hand over;

• 2 Diamonds
  
• 5 Electrum Sheet (You'll need 5 Gold Ingots and 5 Silver Ingots)
  
• 20 Eggs (To make this easier, build a Chicken Coop)

He'll give you a map to a lost shrine. It's located on 220, 167. Note: Don’t go there directly—you’ll only gain access after completing this quest.

Hand over;

• 30 Coffee Beans
  
• 30 Tea Leaves
  
• 30 Celery
  
• 30 Potato

Sadly, you'll have to plant these materials and wait. It's the only way you can do it, but you can build multiple fields and gardens to speed up the process. Incase you're confused where to get the seeds for them, here's the list;

• Hummingberg sells coffee beans seeds. (39, 139)
  
• Hikarishima Lighthouse sells tea seeds. (-137, -14)
  
• Nordweiler sells celery seeds. (-3, 185)
  
• Oxbury sells potato seeds. (233, 18)

You'll need:

• 3 Octopus
  
• 3 Squid
  
• 3 Snow Crab
  
• 3 Lobster

Octopus locations;

• X: 225, Y: 67
  
• X: 180, Y: -102
  
• X: 73, Y: -80

Squid location;

• X: 64, Y: 28

Snow Crab locations;
Snow locations, Kaltstein Mines.

Lobster locations;
Nordweiler, Oxbury, Kaltstein Mines.

If you're struggling with money, mine lots of gold from the Gold Dragon, turn it into ingots, and sell to them to Francis. This can get you to 10K Glims really fast and this really helped me when i needed money to upgrade the stations.
If you see any misinformation or want to add a feedback, feel free to leave a comment! I'll edit this guide if there's any info i missed. Thank you!