Ahem...
For your first year, in Spring, Cauliflower is technically the most profitable, barring the strawberries from the egg festival half-way through. However, there's a limit to how many cauli you can get down in the first half of the month while you're also desperately trying to get all your other infrastructure down, so potatoes are quite viable as well. So, I'd say the number one pick is Strawberries (especially if you can sneak in some Speed-Gro for a third harvest, but even if not it's still two yields which is quite good), then Cauli, then Potatoes. Special mention to Parsnips, the worst yield but fastest iteration crop in the game, never try to use them to get money, but if you can get 5x gold-star parsnips in the first half of the season, it saves you from having to Mass Pumpkin in the fall. Also shout-out to Bean Sprout which, if planted on Day 1, is actually more profitable than even Cauliflower. Of course, getting one down on Day One is... challenging. But you'll want at least one for your bundle completion anyway. Kale deserves a special mention as it technically gives more xp than potatoes do, but potatoes have a chance of a second drop which, while it doesn't grant xp, does sell for more cash. If you're grinding xp, consider Kale as an alternative to mass potatoes, assuming you have at least one potato for the bundle.
For your first Summer, it will depend how much delving and farming you did in Spring. Specifically, how many Quality Sprinklers you managed to grab and how close you are to making Kegs. Because bar none, the most valuable crop you can get in your first summer is Hops... with the caveat that it assumes you are able to brew them all into Pale Ale. Melons are the second most valuable crop you can plant (assuming you haven't unlocked the Oasis and have access to Starfruit yet), and you'll want 5x Gold-Star Melons for your Quality Crops Bundle anyway, so plant away. Blueberries are a staple summer crop because they spam a metric ton of berries, which make excellent preserves. Assuming you have preserves jars available. The other cute little trick with blueberries is running them through a (or multiple) seed maker(s). You make, on average, more money off of the blueberry seeds than off of the raw fruit itself, plus you have a 0.5% chance of getting an Ancient Seed instead (and a 1% chance of getting Wild Seeds). If you haven't found an Ancient Seed in your mining delves yet, this is a way to 'force' an ancient seed for your Greenhouse next season. Don't forget at least one Hot Pepper and one Tomato plant for bundle completion's sake. Also make sure to put down at least one Sunflower, more if you have an interest in dating Haley. And you'll also want to plant Corn on Fertilizer, not for the cash (they're lousy for money) but again for getting 5x gold-star of them for bundle completion.
Fall is your worst season, sadly. Pumpkins and Cranberries are pretty much where it's at. If you complete your Kitchen bundles in this season and unlock the Greenhouse, you can get your industrial scale planting going. Pumpkins and Cranberries both do well in Preserves Jars. Red Gem Berries are kind of a trap. Yes, technically, they are worth 3,000 for the investment of 1,000 for a total profit of 2,000/ea. However, there's a strictly limited number of them available, only two per week in spring and fall, and that assumes you're spending that kind of cash in your first week. Plant one for the Stardrop, maybe a couple more if you have 'em, but they're going to be marginal at best. DO NOT attempt to propagate them in your greenhouse, you'll be losing out on millions per season by doing this with gem berries instead of ancient fruit.
Winter, obviously, you can't plant anything. You'll be subsisting on forage and animal products.
Some goals to aim for:
Spring: The easiest start is a 40 parsnip initial planting on Day 1. Take all the money in your pocket, invest in more parsnips. Watch your stamina and go easy on chopping things down or you might run out before you're done. Do some gathering, maybe some chopping... you're hoping to get Foraging 1 down by the end of the day. Ultimately, you'll want Foraging 6 by the end of the month so you can get Lightning Rods to ward off the damage from summer storms, but if you can manage Foraging 4 by Salmonberry Season, you can double your yield per bush. Once the initial 40 parsnips come up, plant at least one bean starter, one cauliflower, and 40 potatoes if you can afford them. Once the potatoes come up, hold off on planting more until you get 40 strawberry seeds from the festival, and make sure those go down before you go to sleep (hoe and water at the beginning of the day before you attend the festival so all you have to do is run and plant). At this point, salmonberry season starts, now would be a very good time to get your pick upgraded to Copper while you run around collecting as many salmonberries as possible, then spend the rest of the season diving the mines as hard as you can, aiming for level 80+ by the end of the season, at least some gold and a Fire Quartz obtained, and making Quality Sprinklers. Extra batches of 40x potatoes on top of the strawberries can make your profits and your farming skill go faster, but at the cost of stamina which you'll need to go mining. If you have sufficient salmonberries, it's a safe enough tactic.
You'll also want to consider a Silo, then a Coop and a pair of chickens. Ideally you want one white and one brown, for bundle completion's sake. Then get two more, and a couple of mayo machines. This will be consistent profit throughout the rest of your game. You'll want several sheds, plan on where you want to put them even though you probably can't afford any just yet.
You'll also need an Oak Tree stand, and you'll need it down *fast*. Like 30x oak trees planted by the end of your second week. To do this, never touch an oak tree until after you get at least Foraging skill 1, then shake any oak tree you pass by and hoe any seedling that drops near an oak tree. You'll also need tappers on them, preferably by the end of the month. Why? Because you're going to wanting to make Kegs on the industrial scale, and they require Oak Resin.
Summer (assuming you have at least Farming 6 and several Quality Sprinklers): 32 Hops, 40 Melons (on Fertilizer), 40 Blueberries (Speed-Gro will net you an extra harvest if you can manage it), 16 Corn, and whatever else you would like to plant. Generally, that means at least one Pepper, one Tomato, one Sunflower for bundles, maybe a Poppy if you have some apiaries you want to make more profitable, and whatever other assorted crops you'd like for either dating gifts or extra profit. Plant in circles of 8 around Quality Sprinklers. Make sure there's room enough to reach the Hops and surrounding crops, they block your movement. Also don't forget that this is a pretty hefty financial investment for all these seeds on Summer 1, don't go buying a backpack upgrade at the end of Spring and come up short. Your first blueberry harvest should be invested in a Shed to house either preserves jars or kegs. You can fit some 60ish in a basic Shed, and just over 120 in the Big Shed. 60 Preserves Jars would make blueberries WAY more profitable (they go from 50g/ea to 150g/ea, so triple profits!!!), but you really *really* want Kegs because Pale Ale is worth 300g/ea, and hops yields berries daily. You'll need two kegs per hops plant, so that'll be your 60ish kegs to fill a shed. If you can afford two sheds, one for kegs and one for jars is no bad way to start your infrastructure off.
You'll want a Barn to go with your Coop, and four cows, with at least two Cheese Makers to keep up with them. You should also do your best to upgrade it to a Big Barn and have at least one Goat. If you can manage a Deluxe Barn and a pig before the end of Summer, that would be ideal because you need the pig to grow up and produce a Truffle before the end of Fall since they can't produce in Winter. If you can luck into a Truffle from the Cart Vendor, this vastly simplifies your needs, and you can settle for a Big Barn. You'll also want a Big Coop and a Duck, both for the duck egg for the animal products bundle and the feather for the dyes bundle. A Deluxe Coop and a Rabbit would also be amazing, since they are stingy with their feet (which you will need not only for a bundle, but for a couple other spoiler-ish events I won't go into now).
Multiple sheds are the order of the day. You're going to ultimately want at least two sheds with kegs and one shed with preserve jars by the end of Fall, so if you have spare cash and Robin isn't already building something else for her, at least get more sheds down. Really, you'll want those two keg sheds upgraded to Big Sheds, but that can be done over winter.
Fall: Split the field evenly between Pumpkins and Cranberries, with a Yam and Eggplant for bundle's sake. Fairy Rose makes the most profitable honey if you have apiaries. Plant your Gem Berries as well. Oh, you'll also want 10 Wheat down for the fodder bundle. You can keep replanting them and brew it into beer.
The big part of Fall is preparing to shift gears. If you've done your bundles, you'll unlock the Kitchen and the Greenhouse by mid-fall (usually when the pumpkins come in). Hopefully by this point you've gotten access to either the Skull Caves and/or Korobus, because you're going to need a minimum of four Iridium Sprinklers (ideally six of them!) to minimize the amount of space you are taking up. Now is also when you need to decide if you are going to be using Peach or Pomegranate trees as a primary part of your income, or just a sideline. It's the most profitable thing (barring post-game spoiler content) to do in your greenhouse, but it also requires more micromanagement. It also requires a very hefty investment cost up-front if you're getting 30 trees. You'll have to wait until they are grown before infilling with Ancient Fruit and/or Hops, so it's more of a long-game approach. If you want a simple and easy Greenhouse that still will net you a million per season, just fill it with Ancient Fruit and live a one-day workweek lifestyle.
And, of course, more sheds for more kegs. Although at this point, you're probably upgrading existing sheds to put more kegs in them. 116 ancient fruit is 116 kegs needed to keep up with their weekly production once they're fully propagated. That's a full Big Shed by itself. Plus whatever you want to grow outside.
Winter: Continue propagating Ancient Fruit in your Greenhouse, at a steadily increasing geometric rate, until full. Continue harvesting animal products and expanding production facilities to handle Spring's upcoming increased demand on production of artisan goods.
Year Two and Onward:
Spring: Rhubarb is a pretty consistent money maker. If you have any strawberry seeds left over from last season, they're also profitable. Of course, Ancient Fruit will be the *MOST* profitable thing to plant outdoors for the year, as they will produce for all of Summer and Fall with no additional planting.
Summer: Hops infilled with Starfruit. Or, yanno, your Ancient Fruit, which will just now be fruiting.
Fall: Pumpkins and Cranberries. Or, again, the Ancient Fruit if you planted in spring.
Winter: Your Greenhouse still produces weekly, plus whatever your animals bring in.