I will describe each day what you need to build when and how (At least to some degree). Here I will shortly show how it will look like.

Here I will list what to research on that day when the other research is finished.

Build this as soon as you can or when you get to it over the day

Build or do things in the evening after your people have worked. Especially at the first couple of days that is very important because you need every resource you can get.

Things which you should do over the day. Like switch the Warehouse or ask London for a favor etc.

Here I list where to send your scouts next

In later stages we have the book of law again :)

You should not have problems with Hope. Yes it will fall low. But overall it does not matter.

Till day 15 you will have the issue that people want to get rid of you. Let it run for a while and try to mitigate with turning of your Overtime in the night to get under the bar. This should normally work.
Obviously 24h also plays a big role with this. So use it only when you have like halve full discontent not above otherwise you will get into problem.

At the beginning your two medicals are fine. But going forward from Day 4 you will have three medicals but they still not enough. So if you need to juggle the Workshops and maybe a fourth medical. If some people are sick and not in treatment it is fine but you should keep it in balance. Some may die at some point around Day 5 to 8 that is inevitable. From Day 8 onward you should have enough engineers to keep 4 medicals running if needed. From there it should get slightly better. From Day 12 onward you have no problems with medical anymore because you will have two Infirmaries.

At the beginning try to get enough Steel/Cores to fulfill the shipment too London twice. Then you need to juggle between Steel/Cores because you need a lot of Steel but also some Cores for upgrades of the settlements. Use 24h on the Warehouse as often as discontent makes it able This helps a lot with Steel.
I did not use the second tier upgrade which lets you mine Steel/Cores in parallel. First is does not really help you and second it is just one more upgrade which is not necessary. And you are already quite limited on the upgrade path.

You need to get your settlements to Loyal so they can help you in the end. For that just always choose the "Pleases ..." this should be enough.
Hot Springs is the number one which you need to get (and will get) and need to push to a Safe Route. It is your only source for Food and you people need a lot of it. So make it your priority one till you get your route established. After that just check that you have enough Food.
Favors: will be used at the beginning for Food, later mostly for Steel and some Food.
Shipwreck should be your number two. You need some additional Wood and also the settlement can give you Workers which you need for fulfilling upgrades for other settlements.
Favors: will be used at the beginning for Workers, later mostly for Wood.
At last there is the mine. Cole you do not need. So upgrading should only happen sparse. But the favors are really helpful there.
Favors: will be mostly used for Steel

If you built the Cole Thumper with the two Gathering Posts you will not have any problems anymore. You will also get some Cole from the upgrades provided to the Mine settlement.
There is only the point where you collected all the Cole from the spots and you currently researching your Cole Thumper. But this is doable.
Wood is not that of a big deal as some would think. At the beginning you need every Wood you can get. But after that you normally have enough with one Sawmill in the west side and the constant shipments from Shipwreck or the favors from Shipwreck.
Steel is a constant problem. With upgrades in the Warehouse and 24h shifts you can somehow manage it a little bit. But you need so much Steel for all the upgrades and research etc. You need to use favors in Hot Springs and Mine to get as much Steel as possible.
Try to make as much food as you need for your people. If they/some get hungry that is fine. They can go one day without food without any problems. Not producing continuously food helps you in the long run. If they have food each day they will eat it.
Especially when you get to the point when you either make Soup or Sawdust. Just not make all the food at once always. Otherwise you will end up with a lot of starving people and then they will eat your raw food when you get it from Hot Springs. This will make it just a little bit harder in the end.
Because if you can ask Hot Springs for less food favor, you can get more Steel and then you can get more Food from Hot Springs to upgrades etc. You see the point :)

• Faster Gathering

• Workshop as soon as you have resources for it (Build it behind your initial resource depot)
  
• You need to remove 5 engineers already from wood so they can build it

• Medical
  
• Second Workshop
  
• Gathering Post on the road to the Beacon, right before the burned houses
  
• Tents x4 maybe x5 (depending on how much Wood you have left)

• At start people to Steel before the Army Warehouse
  
• All the other people to Wood around the middle

How it should look like in the evening:

• Sawmill

• Cookhouse
  
• Rest of the missing Tents
  
• Second Medical (Move 5 engineers from one Workshop)
  
• Dismantle second Workshop again

• Important: If you have sick people in the Gathering Post, switch them with other people so you get max from the Gathering Post because this is the fastest way to get Wood.
  
• When Steel is empty make your first Scout
  
• Other people to Wood around the middle
  
• 2 people into the Cookhouse.

• Collapsed Building

• Drawing Boards

• Road to Army Warehouse
  
• Administration (Build it above the Tents (in the green zone) which lead to the Warehouse)
  
• Transport Depot
  
• Sawmill on the east side (Should be right behind the Administration, it can happen that you do not have enough Wood for it. Then just build it right in the morning. You will not put people in it anyway before the Wood on the east side is empty.

• If some Wood spots get empty put them to other around the middle
  
• Request Food as soon as you have contact with London
  
• People to Warehouse

• Stone Wall
  
• Back home

• Two Tents for our people from London
  
• Gathering Post to the north (Cole and Wood)
  
• Next Gathering Post further down the road from your first one (Dismantle the first one)
  
• Remove people from Cookhouse and wait for Soup/Sawdust to engage again

• People to the Sawmill
  
• Rest of people to Gathering Post in the north
  
• 24h shift on Warehouse as soon as you have it

• Frozen Den

You will have a lot of sick people and some of them (2-5) will die. That is fine. Do not ask London for Burial etc. First ask for Food again as described below. You should put the last engineers from Workshop to Medical in the night so help a little bit with the mass of people.

• Medical

• Third Medical
  
• Second Sawmill on the West side
  
• Second and third Workshop (Between first and Cookhouse, and one behind the other two Workshops)

• Switch to Steam Cores after 24h shift is over for 2 cores
  
• Ask London for Food (When favor is High), they will give you either Soup or Sawdust. The first couple of batches you want to turn right into your delicious Soup or Sawdust. But further down you should not always produce right away. Let them go hungry a bit then produce more. Otherwise you will end up in the end with a lot of hungry people which will eat raw food directly when you get it.

• Crumbling Hut

• Heaters

• Tents x4

• Important: Move back your 5 engineers to one Workshop you need to finish the medical upgrade
  
• Set Extended Shift on everything when available
  
• Put 2 people back to Cookhouse and make Soup/Sawdust
  
• Your Gathering Post on the road to the Beacon should be empty dismantle it and put people to the north and remaining to the second Sawmill

• Back to town with survivers
  
• Remenant Building

If you really have problems or if they ask to open a new Medical Post, then do it you will get the bonus for Hope and also help the situation a little bit. Just use the one engineer you have left. Maybe juggle a little bit with the others.

• More Scouts

• Gatering Post to the East, right beside the Sawmill

• You should now have enough people to fill all the buildings (except the 3 Workshop)
  
• You should switch back to Steel at some point
  
• Ask London for Corpse Disposal (Build the Snow Pit)
  
• Send Shipment to London as soon as you have it
  
• Enable the Heaters everywhere (Except Workshops). Cole income should be enough.

• Nansens Storm Watch

You will get enough engineers today that you can fill either 4 Workshops / 3 Medical or the other way around. You need to check what is more pressing.

• Brazers

• Tents x3
  
• Switch to Steam Cores again (2 Cores) then back to Steel

• Ask London for Wood
  
• You can move people from one of the Sawmills to the Cole Gathering so you get maximum Cole

• Back to Town with survivers
  
• 1 Scout: Natural Terrace and then further to the Hot Springs
  
• 2 Scout: Windy Beach

• Drafting Machines
  
• Scout Sledge

• Turn of the Heaters except the Warehouse
  
• Brazers x4 (3 for the Tents and Medical, 1 for the Workshops) leave them off for now
  
• Resource Depot for Wood (Build it under the road which leads to the Beacon, right beside the Beacon)

• 2: Overservation Ruins
  
• 2: Tesla City (Do not engage it is to risky)

• Cole Thumping

• Build two Gathering Posts near the Cole deposit
  
• One Brazer for the Gathering Posts

• Send a Building Unit on the way to Hot Springs

• Turn on the Brazers and heating for all gathering things and the medical
  
• Ask London for Wood
  
• Send second shipment to London

• 2: Mirror Lake
  
• 1: Should be going back home after Hot Springs

• Improved Heaters
  
• Efficient Burners

• Cole Thumper (In the area where the cole mine should be)

• Switch to Steam Cores again (3 in total)

• Turn of the additional Heaters so everybody is in orange zone
  
• Ask London for Wood
  
• Ask Hot Springs for Food

• 2: Victims Colony
  
• 2: Back home
  
• Send both scouts to either Wood/Cole settlement

• Infirmary

• You might need to build 1-2 Tents for your new people
  
• You also need one more Brazer

• Ask Hot Spring for Steel
  
• Also try to ask them what we can do for them so you can send stuff
  
• Send already 2 improvements to Hot Spring so you get Food and upgrade to next level
  
• Turn on Heaters etc. so that you still get more Cole then you spend

• Organ Transplant

• Hand Cart

• Infirmary x2
  
• Dismantle two medicals and build Tents instead so you can disable one Brazer

• You should either switched already to Steel or should here

• Use 24h shift if possible with discontent

• Freight Elevator

• Turn all heating off because we have 20°C again
  
• Ask Hot Springs for Food
  
• Switch engineers around depending on how much are sick etc.

• You should be at both settlements
  
• Explore with your scouts the surroundings and then bring them home
  
• Send Building Unit as soon as you have Steel (first to Wood stettelment then to Cole)

• Radical Treatment

You want to push Hot Springs the most because you need to have the Safe Route as soon as possible. But you should also try to do somethings for the other two settlements.

• Mechanical Calculators

• Build one more Workshop and staff when the situation with sick people is ok

• Switch to Steam Cores for 1 whole day then back to Steel

• Ask Ship for Workers
  
• Ask Hot Springs for Food
  
• Ask Mine for Steel
  
• You can most probably dismantle the remaining medicals you have now two Infirmaries. Leave the Infirmaries even if you only need one currently you need them later when Hot Springs/Shipwreck send you there sick.

• Search Ghost Ship
  
• Drying Springs does not need to be searched it is empty

• Overcrowding

• Heater Efficiency
  
• Improved Blowers

• Build Fighting Arenas x3 to cover all our people

• Ask Ship for Workers
  
• Ask Hot Springs for Food
  
• Switch back to Steel

• Dissban one Scout
  
• Other one back home
  
• Then send him on the route around London (Do not go to the bridge)

• Fighting Arena

Depending on how fast you get Steel and how fast you send supplies to Hot Springs you will somewhere around here do the things listed below:

• Depot upgrade

• Ask Ship for Workers
  
• Ask Mine for Steel
  
• Ask Hot Springs for Food

• Send Building Unit to build safe route to Hot Springs

• Child safety

• Difference Engine
  
• Straddle Carriers
  
• Bunkhouse (Till day 23 you should have built Bunkhouses)
  
• Army Warehouse
  
• Infirmary Mechanism
  
• Advanced Heaters
  
• Advanced Burners
  
• After that you can do what every you want but upgraded Gathering Posts and Cole Thumper are quite handy with the cold weather

• Switch between Steam Cores/Steel to your demand

• Ask Hot Springs for Food if you find it necessary, otherwise ask for Steel
  
• Ask Ship for Wood (maybe you need some more Workers)
  
• Ask Mine for Steel/Wood
  
• If Hot Springs ask you to Flood the caves do that you will get 10 more raw food each delivery

• Medical Apprentice
  
• That should be it, you do not need more

That is it. You should now somewhat smooth sail to the response form London. You will then have all your settlements on Loyal. Then you can just rescue it. You just need to provide 250 Steel and 5 Steam Cores which should be doable.