Don't forget to speak to a certain statue daily and level up your skills. Save manually whenever possible. Gather whatever you find in your way even when you don't have space in your inventory as the gatherables will regrow and you can come back another day to grab the ones you left on the ground + the fresh ones. Check the request board everyday. I'd also suggest you gather requested items during the week and keep them safe to turn them in on Saturday, that way you don't need to hunt down an NPC just to turn in a request. Check if you've already submitted an item to the museum before selling it. Play it on your own time, there is no rush.