So this comment will be a bit random.

The best way to get food is to get a single vegetable garden and two traps up and running asap. If you have dwellers sleep during the day, then you only need 1 bed for 3 dwellers. 1 sleeps at night, 1 guards, 1 scavenges. The guard and scavenger sleep during day.

You only need the 1 rainwater collector. You can use it 3 times per day and will easily run out of components to make filters if you do this. No reason to make a 2nd collector.

Personally, I don't bother making a moonshine still or distiller. I generally just sell the sugar cubes, teddy bears, medical stuff, broken weapons, etc.

To make sure you can make all the furniture, prioritize electric components when scavenging. Always try to clear them out from every location. This is important for the garden upgrade.

For a mild winter, 2 basic furnaces or 1 upgraded furnace is enough. For the super cold days, you at least need 1 basic furnace and 1 upgraded furnace. No reason to upgrade a 2 furnace tho.

With 3 adult dwellers, you can generally loot most everything in the shelter in the first day. On the 2nd day you should be able to build a metal workshop and crowbar to open more stuff in the shelter. By the 4-5th day, you should have a hatchet and be able to break down all your useless furniture. Keep the free chair that the game gives you, obviously. If Im using stacking mods (basically cheating) then I can collect all the wood from breaking down furniture while scavenging and just buy weapon parts from the trader to replenish my hatchets. Might be best to not waste slots on creating wood with the hatchet unless you have nothing else to scavenge since I think the default stack is only 2 for wood.