Tips

Early Game

When you first gain control there are some settings you may want to adjust. I recommend turning on "Always Show Tool Hit Location", and setting "UI Scale" and "Zoom Level" to 75%.
You start with 500 gold. Buy some seeds from Pierre's General Store -- Parsnips are a solid first choice since they're ready in just 4 days. Chop 50 Wood and craft a chest for storage, since your backpack starts out very small. Forage wild items to sell (but keep at least one of each type for later use), replant any wild seeds you find, talk to as many villagers as you can, and check trash cans around town for free items.
Fishing unlocks on day 2 and is one of the best sources of early income. Keep any fish you'll need for the Community Center, and sell the rest to Willy to fund more seeds from Pierre's General Store.
The Traveling Cart can start selling Red Cabbage Seeds as early as day 5 of Spring, Year 1 -- worth having 1,000g saved if you're going for a Year 1 completion.
The mines open up on day 5, and you'll receive the Rusty Sword. Bring a pickaxe, gather Copper Ore and Coal, and try to reach at least mine level 5. Start saving 2,000g for a backpack upgrade from Pierre's General Store.
By around day 6, you should have one of each Spring Foraging item, enough to complete the Community Center's first bundle. This is also roughly when Scarecrows become craftable -- make enough to protect your crops.

In general it's a smart idea to keep at least one of each item in some chests. Early on you should sell most things, but keep at least one of almost every item.
Buy an Apple Seedling by sometime in Summer Year 1. You'll need 4 Apples to complete the Community Center. You'll need a Pomegranite too unless you find one in the Bat Cave or the Traveling Card.

Check the Fish Bundle guide before selling any fish. The Fish Bundle is one of the toughest and most time-sensitive in the game, especially if you are trying to complete the Community Center in Year 1.

It's always smart to keep at least one of each item in some chests. Leeks for George, and Grapes for Vincent, are Loved Gifts for them respectively.
Early Game: Any items that you don't need for the Community Center should be sold for extra cash and used for seeds or upgrades.