Okay... let's get into it.
So, first off, we're going to be discussing the difference between
theoretically optimum vs
practicality, because there's a big difference between numbers on a spreadsheet and actually doing it. As a very good example, you have the coffee beans which, by pure numbers, is amazingly profitable. However, in the first place it assumes that you will have access to them immediately, which either requires destroying your save and restarting every friday if a bean is not present in the cart vendor shop or requires somehow getting all the way down into the colder areas where soot sprites spawn and farming them for one. In either case, this is simply not viable for your first spring.
With that in mind, here's some ideas:
First Spring
* Parsnips. They are incredibly lousy for gold per day yield. They are amazing for iteration and thus for xp grinding. Up to a point. One of the more beginner-friendly starts is to take all of the money you got on day one... and invest them into more parsnips, for a total of 40 parsnips planted on day 1. Outside of that, their value lessens tremendously, but this can give you an early kick.
* Potatoes vs Kale. You'll want at least one potato for the community center bundle, but one of the more vigorous questions is 'kale or potatoes', because they have similar growth times. Kale has theoretically better income, but potatoes have a good chance of a bonus crop for generally better profits, albeit at the cost of xp. Your first year will be focusing on infrastructure, and many pieces of that infrastructure will require Farming levels. As such, Kale tends to win over Potatoes in my opinion, but neither are an 'incorrect' answer.
* Strawberries. Do keep in mind that you don't get access to them until the Egg Festival in the middle of the month, so many spreadsheet projections which assume access on day 1 are... not realistic for your first year. Having said that, even with two harvests (three with a certain trick which we won't be getting into because of the difficulty involved), they're still enormously profitable. This can be the backbone of your economy going into Summer, I've seen playthroughs with 40 or more strawberries planted, and done quite well.
* Cauliflower. If you can get the quest reward from the museum for 5x turn-ins for the 9x cauliflower before the middle of the month, planting them is an enormous boon both in terms of cash and farming xp.
* Rhubarb is unobtainable in your first year, so not relevant to this discussion.
First Summer
This is where we start looking at potential processing production, as well as building our infrastructure so that we can be on a better foot going forward.
* Hops. When brewed into Pale Ale, is one of the most profitable crops in the entire game. Also grows on a Trellis, so you need to make sure you can access them all. It will require a *lot* of kegs to maximize its advantage, though. This requires you to set up an oak tree stand as well as constantly heading into the mines for the copper and iron (and coal!) to really get going. If you want to min/max your profits, avoid selling them until you hit Artisan (because let's face it, you *are* going Artisan if you care about money) so they go for 420 each instead of 300.
* Starfruit. Let's get this out of the way now, you won't have the infrastructure, heck you might not even have access to the oasis depending on your play style, to take advantage of this crop in your first summer unless you really know what you are doing, in which case why are you even reading this in the first place if you already know what to do?
* Melons. Staple summer crop, needed for both the summer crops bundle and 5x gold star for the quality crops bundle. Decently profitable. It's good to put in kegs to make wine, but you'll want to prioritize Hops, and you probably won't have enough kegs for both yet. And you'll probably want blueberries going into your preserves jars because it triples their value while the value increase is more modest on melons.
* Blueberries. There's actually several things you can do with blueberries that can be profitable. First is Preserves Jars, which basically triples their profits. The other thing is the Seed Maker, oddly enough. Seeds sell more than the berries themselves, so it's at least an increase in profit, plus it is a way to 'force' an Ancient Seed (something like a half-percent chance for any seed to pop out an ancient seed) which you'll definitely want later. While strictly speaking by the numbers not the most profitable crop ever, it can get you 'over the hump' so to speak. Selling your first crop of blueberries can be used to reinvest in infrastructure quickly. It is good for a quick cash injection.
First Fall
There's really only two crops to talk about here: Pumpkins and Cranberries. Both will likely be going into preserves jars rather than kegs since your kegs will still be processing your backlog of hops unless you *really* got a jump start on keg manufacturing, and both are decently profitable in jars anyway. You'll want enough Pumpkins to ensure not only the Fall Crops bundle completion but the Quality Crops Bundle as well.
From There...
* Ancient Fruit. And it isn't even close. If the only thing you care about is money, this is all you should be planting Y2+ as long as you have the seeds. Which, if you've been propagating in your greenhouse, you should have more than enough for any reasonable requirements. Drown the world's sorrows in Ancient Fruit Wine. Use Deluxe Speed-Gro and use the statue in the sewer for Agriculturalist to be in effect on the 1st of Spring so you get a couple of extra harvests in spring, then respec back to Artisan the day after to continue selling. Over the course of the three total planting seasons, the combined efforts of the best of each season will not match what Ancient Fruit does sum total unless you start getting into niche Qi-exclusive post-game stuff which is beyond the scope of 'practical' or 'reasonable'.
For the greenhouse, there's a separate
guide which was written back in 1.4 but still generally holds true. As a bonus, the basic principles can generally also hold true on your Ginger Island farm plot since it functions like a greenhouse in that everything is always 'in season' there.