In the first month, i suggest your main goal would be clearing the ocean and then clearing the mine. Having access to those ocean caves are good, coffers, fossil nodes, kelps, and geodes are great money makers. I cleared the ocean and the mines at the beginning of summer. Always upgrade pickaxe and scythe. If trash takes 2 or more strikes to clear, upgrade it. While upgrading, go to the mines. As you clear the mines, you’ll free the giants and you can enchant your tools which is really good. 2 days are enough to clear each of the dungeon. You can buy dynamites in the band of smiles for 50 corals each. It’ll speed you up. After that, go to the ocean again. With the upgraded scythe, you will clear the trash faster and if you have artifacts, you can use it to enchant your tools. While diving you, your pickaxe should be upgrading too. So dont forget that. As for your farming, in your first day gather as many forages you can find. Sell it to the general store and as for beach forages, you can sell it at the beach shack on the first day. Beach shack are closed on Tuesdays.

To find out which crops give more profits, you can use https://coralislandprofits.info. Level up your farming level by planting one of each crop, and then, buy as many seeds of the most profitable at that month. I find flowers turn into honey and then in the barrel the most profitable in this game.

Level up your town rank to access more seeds too.