General: "Rules" I followed:
Fulfilled every request! Heating, food, shelter (choose the easiest one that you can DO),
Right at the end you may get a request for "Coal Shortage". This is the ONLY time you can say "we will do with what we have" (basically refuse it).
No one died at all (not even scouts)
There normally IS 1 scripted amputee, sign the prosthetic law right away to avoid him from killing himself!
Rescued everyone, and sent scouts out to collect every refugee group (This ALSO includes the 5-8 camps/locations you will find Right before the storm hits).
Never cleaned graffiti (ignore it)
Always let the Londoners speak (You won't be signing the last law or allowing faith keepers or police, so you can't do this anyway).
If the Londoners do leave give them food (You can normally stop them with hope before they actually leave though).
Slowed down automatons (if someone is injured)
Gave the father food to look for his daughter
!!!!!!!!(THIS IS A REQUIREMENT! If you do not do this he will hang himself and the achievement will be voided)!!!!!!
Gave the people wood when they complain before the final storm hits (save about 1,500 - 2,000 (mine was 1,800))
Abandoned lower levels of the coal mine (When final storm hit's you will have an option to abandoned the lower levels of the mine or send 10 people in. Abandon it as people ALWAYS will die).
Various other "good" responses
Before the final storm you should have: 630-693 people
I just got Golden Path on Easy. Hope this helps. (This uses Faith, see the attached answer below for the Faith alternative)
Double Rations for the Ill
Optional (NO ONE SHOULD DIE IN YOUR PLAYTHROUGH!):
House of Prayer
Ring 1, 2, and 4: all houses
Ring 3: House, House, Watch Tower (repeat)
Ring 5: Overflow housing until the very end, then destroy Ring 3 Churches, and replace them with Houses
Other: Tons of child shelters (I had , care houses, hospitals, and infirmaries.
Heat: Noone ever in frostbite conditions except for 1-2 hours at the end from the storm.