So what are people's thoughts on starting build orders for Frostpunk? I really feel like the first few days set the pace for the rest of the run, so a strong build order is what really makes the run. I'm not happy with my hard difficulty build orders yet (I either walk the golden path without deaths, or try again. So far Arks is the only one I've succeeded to those standards on hard difficulty), but I think I've got my normal difficulty builds more or less perfected. Here's my approach for New Home:

(I even made a video! I cringe when I look at all the little mistakes I made because I was going quickly and didn't want the video to be me pausing every 30 seconds, but I think it communicates the build order well enough)

Buildings
To priority is a gathering post to collect wood and steel scrap. When it's done, reassign your workers to quickly build a second gathering post for the other wood and steel scrap as well as a hunter's post. Emergency shift on one of the gathering posts, and use the wood income overnight to build a cookhouse, a medical post, and two workshops. The following day you'll build four tents to satisfy your people's needs and the beacon. I screwed up my build order in the video at this point; you should wait until the beacon is done first before building the tents because your workers will prioritize building structures near to the generator, but the beacon is your priority. Wait until it's done before plotting down the tents.

After this, put up three sawmills so you have workplaces for your refugees, a gathering post near one of the two piles of coal, two more workshops for your new engineers, then more tents and a medical post. At this point you should be grabbing refugees like crazy, but three sawmills will produce enough lumber to keep building more tents and workplaces. You'll want to build more hunters posts (your initial food reserves should be running very low at this point) and steelworks because the steel scrap will be running out at this point. Once all of that is taken care of, beeline for the infirmary and put up more workshops.

Technology
I'm pretty much convinced at this point that your first tech should always be the beacon. If you have a build order prepared, getting the extra workers immediately is simply more valuable than any other tech. After that, sawmill is the next priority to ensure you have workplaces available for the influx of workers your scouts will bring in. Hunter's gear is next priority after that, since a 33% increase in productivity is way better than any of the other 1st tier techs. The next stop after that is to go for the second tier of techs so you can grab the second scout team to help round up the last of the refugees. Then pick up the steelworks and tech up again for the infirmary and hunter's tactics. By this point you should have all the refugees and solid resource income and can trigger the Winterhome event.

You'll need to pick up some form of coal mining for when your coal patches run out, but because heating upgrades really aren't necessary on normal difficulty you can delay that for quite some time. Otherwise your tech priorities from this point on are to balance scout upgrades, steelworks upgrades, and housing upgrades. Sawmill upgrades are unnecessary; in my experience, you tend to bottleneck on steel anyways so if you upgrade your sawmills you'll just end up with too much wood. The big thing is that you don't want to stop for extraneous techs, because you really want to beeline to full housing of your entire population.

Laws
Emergency Shift. Immediately. The extra resource income at the very start of the game it provides is simply way too good to pass up. And I really do mean "immediately", because you want to have your second law passed before the start of the second day, and that law is soup. Being able to convert your starting raw food reserves into soup makes it last longer, and means you can delay hunter's posts for a while. This is important because hunter's posts are very inefficient until upgraded, and soup lets you delay building more hunter's posts until you've got those upgrades down. After soup, you want extended shift. At this point, I don't feel the order in which you get laws really matters, you just want to get as many passed as possible before Winterhome opens up the new options. I would advise against the cemetery at this stage, though; it gives a massive boost to hope, so save it until after Winterhome.

On Hard Difficulty...
Edit: aaaand on my very next playthrough I nail it. I haven't completed the run yet, but I've convinced all the Londoners to stay with several days to spare, giving me lots of extra time with which to just expand my economy. I can't remember my exact build order, but the big difference this time was preemptively putting up three medical posts to keep my people healthier for a bit longer while I moved for infirmaries. It's still a lot slower than normal difficulty, but it still stabilized nicely after Winterhome.

What I originally said:

The hard part I'm having with hard difficulty is getting the infirmary up early enough. The lower initial resources and collection rate means that feeding the generator actually takes a fair bit of manpower, and also requires you to toggle it off during the day. Combined with the difficulty setting, this means people get sick more often (which means they aren't working)... I just can't get that infirmary out early enough while still going full throttle on the economy. I think if I could solve that problem then the rest of hard difficulty would fall into line easily. Every single worker devoted to expanding your economy versus maintaining what you currently have is a big deal, and those advantages snowball. I feel that if I could get to infirmary without compromises, the entire run would be in the bag. I just haven't got a build order that does that yet.