Continuing from yesterday, the next part of the game is either "go into town" or "go to Topham's area". I'm guessing we go to Topham's first, because that unlocks some things in town.
1. Call Nancy's dad and learn about telegrams. I'm pretty sure if you ignore this, he's going to automatically call you at one point. That would mean it's faster (and cheaper) to NOT call Dad at this point, but maybe I'm forgetting something that makes it advantageous to call now.
2. On the road to Topham's, get the piece of paper about the key at Waddell's. That way, when you go into town, you can get the key appraised and solve the clock puzzle at Jim Archer's.
3. Find the mouse for the cat.
4. Talk to Topham. Solve his puzzle. I'm pretty sure he won't let you explore his house without solving his puzzle.
5. Solve the clock puzzle on the mantel for a mirror.
6. Read Josiah's notebook of clues. I'm pretty sure you can't solve some of Josiah's puzzles, without having read the notebook. The big puzzles would be the trivet puzzle in town and opening the carriage house door.
I said "I'm pretty sure" multiple times. When routing the speedrun, I'd have to test it and make 100% sure. Because if it turns out I can solve the carriage door puzzle without getting Josiah's notebook? Pfft, I'm not doing steps 4-6. I'm skipping those.