Spring will by far be the most challenging month, you have zero skill, a huge amount of work to do, and the lowest profit margin.
Clear all weeds!
Build a silo!
Build a coop and buy chickens!
Build a barn and buy cow!
Upgrade your bag to 24 slot!
Upgrade your axe to copper!
Hit level 40 in mines!
Fix bridge on beach!
Get the farm cave running with fruit bats!
Build preserve jars!
Finish crab pot bundle to get crab pots running!
Or
Make friends with Caroline and watch the cash roll in
Wild Horseradish
Daffodil
Leek
Dandelion
Parsnip
Green Bean
Cauliflower
Potato
Gold star parsnip x 5
Sunfish: 6am-7pm, sunny weather
Catfish: 6am-midnight, rain
Shad: 9am-2am, rain
Largemouth Bass: 6am-7pm, Any
Carp: Anytime, Any
Bullhead: Anytime, Any
Sardine: 6am-7pm, Any
Bream: 6pm-2am, rain, rivers
Eel: 4pm-2am, rain, ocean
First thing you need to do is clear some planting space. You are given 15 parsnips and 500g to start things off, clear enough space to plant all those seeds, then start clearing weeds. I cannot stress this enough, you must clear the weeds, for two reasons:
They have a chance to drop seeds, your first crops will depend heavily on those seeds, try to get enough to have 2 full plots of 9 seeds each at a minimum, that means you need 3 seed drops from the weeds.
If weeds are left to grow they will damage your farmland and impact your bottom line. The first couple days almost all I do is clear weeds, then keep an eye for them, they like to hide in the grasses and you need to eradicate them. If you want to use the tea saplings for cash generation you need a lot of fiber, each one requires 5, so collect and keep every bit you get.
Second thing you need to do is build a storage chest, this takes 50 wood and is a recipe you already know. Chop down a couple trees and get that chest, you only have 12 storage spots in your bag and will be picking up a lot of stuff, you need to store this stuff.
With the crops planted and chest made, stow what you don't need (I always try to carry my scythe and hoe with me the first few days to clear any weeds I see and dig up artifact spots) and head to town. Start foraging now, pick up anything and everything you see.
In town go to the store and buy more seeds, its a bit of a risk until you get a scarecrow, but I usually pick up 9 potatoes (450g), these are your big cash crop for spring; they mature in 6 days and are great value on the market, despite being an expensive seed.
Make as many introductions as you can, you have a quest to get to know everyone as it does come with a little cash when done. I also make a point of meeting and talking to Haley and Caroline the first day, if you have found any daffodils, they make great gifts for both of them. A little effort with Haley makes sure she will dance with you at the end of the month and set you up with a wife by the end of summer. Other than the daffodil needed for the bundle I keep all of them for gifting. On the same note, anytime you are out and encounter somebody make a point on talking to them, each chat give a little friendship and it adds up.
As previously stated, Caroline gives you the tea sapling recipe. Once you are at 2 hearts with her and visit her in her sunroom (any day between 9AM and 5PM when it's not raining) she will send you the sapling recipe; the sapling is relatively cheap to make (2 wild seeds [any],5 fiber, 5 wood) and, once planted, for the final week of each month (day 22-26) will yield a tea leaf each (50g); if you have kegs they can be distilled rapidly, doubling the price. They require no tending or watering and can be used in place of fencing, great as it never needs repairing, but the real money is in selling the saplings themselves (500g each)
Always be foraging, except for tree seeds (until you hit level 1 you'll only destroy them trying to pick them up) as you'll want to save them until you know how to make Field Snack. Once back at the farm plant your seeds and make sure everything is watered. You'll likely be low on energy, but fortunately it takes no energy to use the scythe so go clear more weeds, take some grass too but not too much, yet. Keep at it until about midnight then head to bed.
Day 2 is the start of the repeat cycle, wake up, check the tv, water your crops, and do a bit of clearing. You'll have a letter to meet Willy, so head down to the beach to get your rod before 5 that day, talk to who you can, especially Haley, catch a fish or two, and head back to the farm, making sure to forage along the way. At the farm I like to spend a couple days clearing wood and stone, they take a lot of energy, but return needed material and help clear the land, slowly but surely. If you can, plant another plot of wild seeds. Keep pushing, eat some foraged food to keep going, and sell what you don't need, making sure to reserve the required stuff for bundles.
Make sure to check the island in Cindersap Forest due south of the farm, there are often spring onions growing there that are good for some extra cash, but are also great for replenishing energy depleted by hard work when there is still time in the day.
Day 3 is your first rainy day, you could fish, great way to make money and get some bundle fodder, but I like to use it to continue clearing the farm. Start cutting a couple more trees and continue getting rid of rocks and wood, maximizing your energy usage while you don't need to water the crops. Go foraging, visit town and chat with a couple people, this is your life now.
Your first harvest will boost you to level 1 farming and give you the scarecrow recipe, which you need to keep crows off your crops, and some cash to buy more seed; split it between parsnips and potatoes again, but also pick up a few bean plants. Beans are expensive but continue to produce and are required for a bundle, I usually grow 3 of them at a time.
A couple days later the community center will open, after the cut scene go inside to trigger the bundles, you can't do them yet, but you need to get this started. The next day will be a visit to the Wizard, which will take you past the vendor, and will allow you to start making bundles. First one up is the spring foraging which will give you 30 spring seeds, I plant most of them, saving a few for filler rows here and there as needed. You'll be very busy watering for a few days, but the harvest does pay off well. A note on the wild seeds, planting and harvesting them will help level your farming skill, but using them to make tea saplings will generate cash, which you do depends on your play style.
By now the mine should be opened and you should have the cash for a backpack upgrade, its expensive, but worth it, especially in the caves. Once you've been down there a few times you'll be able to craft a furnace and smelt a few copper bars, so you should build a silo (100g, 10 clay, 100 stone,5 copper bars). Having a silo will allow you to start mowing hay and store feed for the animals you will soon be picking up, I like to put it beside the cave, out of the way.
The mines also make the archeology quests viable, opening geodes gives artifacts that can be contributed to the Library which gives rewards, among which are cauliflower seeds. You need a cauliflower for the spring crop bundle (I like to keep a gold star cauliflower for the Summer Luau as well) and they are profitable, although the seeds are expensive and the growing season is too long to make them a great cash crop (in my opinion, but you do you).
With a few more bars of copper you can start making tappers (40 wood,2 copper bars, foraging level 3) to collect tree sap, make at least 3 to get one on a pine, maple, and oak tree, respectively; you need all for bundles, and the oak resin and maple syrup will be important for crafting later. I like to plant 2 of each type of tree by the water bowl, behind where the chicken coop will eventually go, to start a little tapper orchard, but I usually end up spreading them around in an effort to get all the oak resin I want to have for the many kegs I'll eventually build (more on that next month).
By the end of the second week you should be able to buy a coop (4000g, 300 wood, 100 Stone) and two chickens (800g each), a brown and a white. When you purchase the chickens pay attention to what Marnie gives you, they are mostly white, to make sure you get one of each, take the first one, then start the purchase dialog, she will ask you to show what coop the chicken should go in, if it is not the other color, close the dialog and start again, keep doing this until you have one of each color. You now have a new daily task, checking for eggs and petting chickens.
With chickens giving eggs you should get a mayonnaise machine (15 wood, 15 stone, 1 earth crystal, 1 copper bar, level 2 farming), or two, going, as it substantially increases the value of the eggs produced. The mayo machine requires farming level 2 to learn, and if that's an issue to reach by now, maybe Stardew isn't the game for you?
Don't miss the salmonberry harvest, great way to make spare cash, or keep food on hand. I like to keep a largish stack of berries on hand (50 or so) for food and preserve making when it comes available. They don't sell for much (5g ) so they are good to stockpile and increase on value.
Do the Robin's Lost Axe quest, which pays 250g that you can use, and gives friendship. On that same note, make sure you are keeping up with all your friends, especially Haley, and gifting her the 2 daffodils a week to get those hearts up, you need 4 with her to get a dance. The Easter egg hunt occurs mid month, show up and collect 10 eggs to win and get a hat.
By now the crops should have settled down into a nice little cycle of water, harvest, buy seeds, and replant. Your farm should be nicely cleared, at least of weeds, rocks, and sticks, and you can start focusing on trees. This is a good time to upgrade your axe, makes chopping easier and lets you remove the hardwood stumps (you need 10 hardwood for the construction bundle). You should have lots of time to devote to fishing and mining, so push to level 40 in the mines by the end of the month and take advantage of rainy days to get the fish you need, some of them, like the catfish, are a tough catch and may take a couple days to get.
The crab pot bundle is important but can be tricky, you want the crab pots it gives to start generating passive fishing income, but it depends on some RNG at the beach. I've seen times where the Cockle is not available until late summer, and you can't get the material to build your own pot until you get past level 40 in the mine, so while I say you need to have it, you might not be able to. Same goes for the crab; easiest way to get it it is killing rock crabs in the mines, but they don't always spawn, and the drop rate when killed is kind of low. Still a great goal to have for the month.
Final thing for spring, build your barn (6000g, 350 wood, 150 stone) and get a cow (1500g). Buy a milk pail (1000g) at the same time as the cow, if you can, you won't get milk for 5 days, but you will need it, and it can be tough to find Marnie doing her job when you need her. Try to have a minimum of several thousand g on hand for summer seeds, this will be an expensive season to get up and running, but once in place will be a great base.
Along with the cow, you should also get a cheese press (45 wood, 45 stone, 10 hardwood, 1 copper bar, level 6 farming) built, like the eggs, cheese is worth more than milk, and not a tough machine to make. The only issue with a cheese press is you must be at farming level 6, which could be an issue depending on how much farming you are doing; if you are splitting your attention with the other stuff you might not hit level 6 until sometime into summer, not really a problem, but something to be aware of.