The Island provides opportunnities to fish, dive, collect insects and foreign fruits and book tours to other Islands where specific mini-games are held. Furthermore, there is a shop at the Island where furniture and accessories that cannot be purchased anywhere else are sold.
You must meet Tortimer before Kapp'n will appar at the wharf of your village with his boat. In my game, I believe Tortimer appeared on the fourth day or so of gameplay. At that point, I had paid off my initial debt to Nook and upgraded my house once. More importantly I had 100% approval rating with my Neighbours.
I do not know yet if there are Fish on the Island that cannot possibly be caught on the beaches of your home village but I do know that rare and valuable fish appear more often there.
Two types of 'foreign' Fruit can be found on the initial island and more can be obtained from the Islands where the mini-games are held. I suspect that the two types of Fruit found on the initial Island do not vary but the Trees that are loaded on the Islands with the mini-games may be random as I found Mangoes on my first visit to participate in the Fossil Hunt and Lychees the second time. I am keeping a log...
You can plunder both the initial Island and some of the Islands with mini-games for Flowers as you do not need any tools to pluck a Flower or shake a Tree for Fruit, but there is one huge disadvantage to a strategy of stripping the initial island of Flowers. Butterflies and some other insects that are attracted to Flowers no longer will appear. One therefore should sestrict flower collecting to the mini-game Islands. If you need more Flowers on the initial Island, collect some during a mini-game and plant them when you return to the main island.
There are a few rules to diving. As there is an entire chamber in the Museum devoted to items obtained when diving, it is useful to master the technique.
The first thing to remember is the fact that the Items that appear as dark shadows on the floor of the Ocean are time-restricted. There are two controls that you can use when you are wearing the wetsuit: A and Y. The A Button will allow you to move freely through the water. Press Y when you wish to dive. After doing so, you will be able to move underwater for a brief interval by pressing A, but your movements will be very sluggish and most creatures will be able to outrun you. There are limits to the area where you are allowed to dive as well and often creatures will escape beyond the buoys and lines that act as a fence for divers.
To maximise your success, it therefore is best to use A to swim until you are literally on top of the shadow, then dive using Y and promptly collect the Item.
Some of the items you can obtain when diving include:
Flatworm: 200 Bells
Octopus: 1200 Bells
Chambered Nautilus: 900 Bells
There is a Diving Category in the Items List Guide.
After a week or so, a Wet Suit appeared in the little Shop on the Island. It was a Green West Suit and it cost 40 Medals. After buying it I was able to explore the seas off Asgard and catch the same Items I had found on the Island when diving. The next day, a different style of Wet Suit appeared in the Island Shop but, although it was more attractive and elegant than the one I purchased but no more useful than the first.
One of the advantages of having a wet suit in your own village is the fact that you can find Scallops in the water that will bring Pascal to the surface. These are NOT the same Scallops that you find on the beach incidentally as veterans of Animal Crossing will be aware. It is possible that Pascal might appear on the Island but I am very doubtful of that.
You actually should regard the Island as you do your own village in terms of growing Fruits, Flowers and keeping the Beach clear. If you do not collect the Shells that appear on the Beach and leave Fruit on the Ground, ultimately no new Items will appear. As previously discussed, bringing new colours of Flowers to the Island from the mini-game Islands will cause more Butterflies to appear.
Furthermore, it is possible to use the Shovel to plant foreign fruits from the Mini-Game Islands. You therefore will have another area where more than one foreign fruit can be harvested regularly.
In terms of how to rid onself of items collected or caught on the Island there are three different possibilities that make sense. The first is to stash them in the wicker case for transport back to your village. There are four different pages of slots, 10 to a page, where items can be stashed. This gives you ample storage space for any valuable items as well as many that are not so valuable as you are given a total of 40 slots.
Anything that is placed in the case must be removed at the pier in your village. Although you are warned to collect your items prompty, it appears that they can be left safely in the case for a couple of days. The real problem is lack of space if you choose to return ot the Island without having emptied the case prior to departure.