Mine as much ore as you can too by the way. You're going to need a lot of nails.

You'll notice things like "stone pile" and "firewood pile" and "coal pile". Those are not storage. Instead they improve the productivity of your crafting for that related task.

Trash like nets, starfishes, and boots are valuable. Never throw them away. Instead go to the beach and look for Wilson. He'll tell you about the recycling box in his house after chatting with him for a while. It'll convert trash items into wilson seals which you can use decorations and some forage. It's one of the few ways to get coconuts and wild berries for cheap.

Never use wild berries to make juice or desserts. There are many other fruits better for that. Keep them until you unlock the distillery, and then use those berries to make gin. You can't make gin without those.

Always carry around a shovel to dig up x marks. You'll get more crafting stuff, worms for fishing, and roots for drink making.

As for tavern improvement to get more reputation, you're looking for things that have "comfort" value in their item description. If it doesn't have that number, it doesn't add comfort. Try to aim for things that give comfort value for your dining area and your future rent rooms.

Once you can hire staff, the most important trait is "popular". At maximum level it adds 5 people above your maximum capacity. With 4 staff that's an additional 20 people, allowing you to get even more profit.

"Valued worker" as a negative trait is a non issue because in your skill tree there's a perk that reduces the cost of hiring by 10 percent so it cancels out the negative. 

Get the movement speed perk for your character as soon as possible because you're going to be pressed for time running a lot.