Nearly everything on the island is movable later, including all buildings and even cliffs and rivers. The main things that are fixed are the stuff on the border of the island (river mouths, beaches, rocks/peninsulae, the dock and the airport) and the resident services plaza, so picking your island layout should be based around that primarily.
The starting week or so is a bit slow and tutorialized, with a lot of things unlocking day to day. Try to do everything you can as they're presented to you to keep things moving (particularly: donating critters, building the museum/shop, and building the three new villager houses). You'll need 30 iron (as well as some other materials) to build the shop and a little more to build houses the next day, so save up!
If you want a bit of a jumpstart, after day 2 you can travel to other player's towns and buy recipes for tools you don't have yet from their shops. You'll get them pretty quickly during the tutorial, but if you're impatient (or just want to get across the river to build stuff there instead of moving it later) you can do that.
Eating fruit is important, but so is not eating fruit: if you have food in your stomach, you can transplant trees by digging them up with your shovel but you can also break any rocks on your island by doing the same. If you haven't eaten, you can instead get up to eight items from any rock by digging holes to keep yourself from being pushed away and whacking the rock as fast as you can. Rocks do respawn (at a rate of 1/day), but as they're your main source of iron/gold you don't want to go breaking everything you see.
To get the Able Sisters to move in, you'll have to build the shop first. Mabel will appear in the following days, and you'll want to spend a bunch of bells buying clothes to make her think moving in will be a good investment. If you've spent at least 5k (this number is fuzzy, so go over if you have spare cash) she should talk about moving the next day you see her.
The left and right arrows on the D-pad seem to swap between tools based on their relative position in the inventory rather than the tool ring, so pressing it will move from the current tool to one left or right of it in your pocket. I mostly found it useful to link the axe and net in case I ran into wasps while chopping trees, but maybe there's other combos. Pressing and holding A while floating the cursor over an inventory item will let you move it around.
The */10 that shows up when you eat a fruit is a bank of fruit-specific actions you can do, which seems to consist solely of digging up grown trees with the shovel or breaking up rocks. It's handy while moving trees since normal actions like weeding won't waste your fruit, but if you want to avoid breaking rocks for better yields as in an earlier tip, the easiest way to zero it out will likely be to dig up and re-plant the same tree over and over.
Holding B allows you to run. It does make you likely to scare away nearby fish and insects, so consider when to use it.
Holding A while the net is equipped locks you to sneaking speed without having to worry about tilting the joystick too far.