I'd start by clearing space and hoeing and watering a dozen plots then plow the starting cash into buying and planting 12 radishes at 40g a pop, to get farming 1 for the scarecrow. Also chop enough wood for two chests, one of which goes at the farm to leave your tools in.
Then get the rod from Willy and fish the rest of the day at the mountain lake, taking the remaining 50 wood for another chest and putting it next to the fishing spot to store what you catch as you can't afford the backpack upgrade yet.
Skip Luau on the 11th and fish the lake all day. Keep the chubs for food, save the rest for cash when needed.
Day 12, I'd chop trees (cut off treetops only, leave the stumps for now) to get 300 wood to repair the bridge, and then get all the special beach forage too, that's more good cash. I'd also sell some fish to Willy and splurge on the 24 slot backpack.
Day 13, guaranteed stormy day, get that beach forage again, and forage the rest of the map because it's Saturday.
Day 14, I'd grab the last day of extra beach forage, and if luck is good I'd chop 50 more wood for a chest in the mines entrance and progress down some levels, but if luck is bad, just keep fishing, cos you can't have too many chubs to fuel yourself
Day 15, I'd be really just want to get some way down the mines even if luck isn't great
Day 16, radish harvest day. Get them up, clear lots more space and hoe water and plant as many melons as you can afford after selling the fish. You want to plant 125+ to allow for losses. Plant them today, even though you might lose a couple overnight to crows, because that's a price worth paying to harvest them on the last day of summer, and you can craft scarecrows in the morning.
Day 17 onwards, after crafting your scarecrows and watering your melons, just get descending in the mines, because you need to hit level 80 to get gold ore. Fish all day on a bad luck day, and you should earn enough to buy enough salads for fuel for the rest of the month.
Day 18 to 27, keep everything watered and keep descending until you get to 80. Farm ore and smelt for quality sprinklers. If you run out of food, spend another day fishing and sell for salads
Day 28, harvest melons, but don't sell them. Pick Tiller overnight
Fall 1, you should have hit Farming 6, so make Quality Sprinklers and lay them out. You don't need to water today. Sell the melons direct to Pierre and buy and plant pumpkins, and you can harvest and replant on Fall 15. You should have plenty of cash left over for whatever use you have for it