Clearly Don't Starve is a sandbox game, and you have quite a bit of freedom to play the game as you please. (Quite frankly, I've spent a lot of the time wandering around the game fairly aimlessly.)
But, I'm wondering if there are certain tasks that should take a higher priority within the first 20 days.
Clearly, building a Science Machine and/or an Alchemy Machine are very high priorities. And, next I typically have been trying to acquire some warmer clothing.
But, where should I be focusing my attention from here?
Should I be building structures? Farms? Exploring the landscape?
Basically, I'm looking for a Quick Start guide to having a successful long game.
Best Answer
You said it, it's a sandbox game. Do what you want, there are a lot of different ways to survive 100 days.
Since you specifically asked for the first 20 days (and winter hits on day 21, so that's convenient), here's a small checklist for your pleasure. Feel free to edit in stuff you think is missing:
Days 1-5: gathering
Explore as much as you can, gather food to stay alive, and some basic resources:
Find a balance between picking up just what you need & picking up everything you can. You'll want to cover some ground.
Days 6-10: settling
Building a small camp to ensure food production. You'll be needing manure, so close to beefalos (or a pig camp) is advised.
Days 10-15: improving the camp
Explore the lands around you, bring the good stuff to your camp:
Days 15-20: prepare for winter
Winter is coming. It will be cold, you'll find it harder to find food & sanity.