The power to crush stone
You will be getting all of these important materials from stones. Stones are, well, stones. They appear on your island, and you can whack them to have materials pop out - oh, they might also have bugs pop out, too.
You can actually crush and destroy stones in this game. Simply eat a fruit, and you'll be given the power to unearth trees with a shovel, or crush rocks. But you should avoid doing this at first, at least.
Hit a rock with a shovel after eating fruit, and it'll break, revealing a single piece of material. Hit it without eating a fruit though, and you'll be able to hit it multiple times within a few seconds to get multiple materials. Plus, if you break all your rocks, you won't be able to harvest them day after day.
Two holes, eight nuggets
All you need to get what you want from stones is two holes dug out with your shovel. Basically, once you first hit the stone, a timer starts ticking down. With each hit you can get more materials, but if you get pushed back, you will have to walk forward to hit the stone, and this will cost you materials.
All you need to do is dig a hole directly behind you, and another hole next to that. Then wedge yourself up against the rock and the hole, slightly on the side where you have the other hole.
When in the right position you will get wedged between the two holes when knocked back, and you can keep hitting the rock up to eight times, getting material for each hit. This is much better than getting three or four materials each time.
New stones every day
If you do end up breaking all of the rocks in your town, never fear. They do come back, thankfully, but they will come back at a rate of one per day. This means it can take a while if you've broken everything down for stones.
But one of the rocks on your island will also be a money rock once per day. Use the two-hole strategy detailed above, and you'll be able to get several thousand bells from the money rock, as the amount of bells it gives increases with each hit. Only getting a few hits in can cost you thousands.
Make sure you travel your entire town every day using the two-hole strat to hit every rock eight times for both materials and bells.
Nook Miles Tickets
Finally, we have the Nook Miles Tickets. Now, when you've smacked all of the rocks on your island in a day, they're done until the next day. Inconvenient if you're in need of more iron nuggets, or whatever else.
Luckily, for 2000 Nook Miles, you can purchase a Nook Miles Ticket from the machine in the Resident Services Center, and that ticket can be redeemed at the airport you arrived at so you can visit a random, small island.
You can find bugs, fish, and even new villagers on the islands, but most important are fresh rocks, with fresh materials to harvest. You know where this is going. As long as you have the Nook Miles, you can keep flying to islands and harvesting all of the materials from the rocks you find.