There is no one correct way to advance in the game, and also it's a game, so if the thing you're working on currently is annoying, go play a different part of the game for a while! Tired of farming? Let your fields be empty for a season while you kill stuff in the mines. Tired of chopping down trees? Spend some time fishing. Tired of rushing through quests? Ignore them and go around talking to your favorite villagers.
One of my goals is to unlock the greenhouse as early as possible, because then I don't have to worry about rebuying seeds and keeping track of planting schedules, I can just fill it with something that regrows and have a steady income from it.
If you're like me, you start running out of trees to cut down for wood at some point. So before you get to that point, take a day to slap down a million tree seeds somewhere villagers don't travel much, like the south parts of the woods, the desert, or the top and right part of the railway. Then just forget about them until you have that moment of "oh no, I'm running out of wood!" and then you have a nice backup forest waiting for you.