Money is realtively easy to come by and by spending it on the store you will be expanding your collections and materials much faster. Try to buy what you can from the daily selection, specially fruit trees, bushes and flowers. Even the most common items like wood, branches and nuts: get them! They will come in handy for crafting and cooking. Trust me. Also, spending money is one of the easiest achievs.

Potatoes might be really common, but the moment a quest or task is asking for one you will struggle to find it. If you always have one of each thing, they will be ready to go the moment it is needed/requested. That being said, don't hoard. You don't need ten mushrooms in your storage. Burn them and cook them to expand you collection faster.

Fish and critters are always in abbundance and by catching them you will also be doing some grinding towards certain achievements. Burn the fish in Flamey and sell the charred bones.
The absolute fastest way to get a lot of coins is by recycling quartz! You'll probably have many more that needed at the beginning anyways.

At first I was clicking and clicking away until I realised that tools like the shovel, the pickaxe, machete and others can be used so long as you keep them in your backpack. Things started to go much faster from there.

I could have saved myself some trouble of changing tools repeatedly by just reading with more attention, but if you're like me, know that you can press:
[1] to automatically put the fishing rod in your hand,
[2] for the dowsing rod
[3] for the critter rod. (Specially useful if you're trying to catch a fast critter)

Look at the shadows in the water. Some of them don't have fins and could be materials (kind of rare ones at that) and recipes. You can fish them too.

SPOLER: Slightly ahead of the game, some different shadows without fins will show up in the water and they can be fish that have a specific technique required to fish them.

Most things, while blending nicely with the scenery, are pretty easy to notice. What I wish I realised sooner is that there are trees and rocks and the likes that can be found naturally around the island and you can use them by simply getting light to them. Could've been harvesting those much sooner!
Look around and put you cursor on top of stuff. If the cursor changes when hovering over something then you can interact with it.
Look in new areas eveytime you expand the island. New things might come along.