Rogue Legend

Each season is 20 days, and after the 20th day, all seasonal crops (everything except hay) will die. Crops typically take 6-10 days to grow before you can start harvesting, so don't plant anything after day 15. For spring plants at least, the strawberries are valuable as food. Everything else should be sold. Scavenging for berries is quite profitable (once survival's not an issue), especially after you clear the wilderness and can travel quickly. For winter, 2-3 chests of food is more than enough.

Whenever you get a bunch of a new ore, the sword and shield are the most important tools to craft (after the backpack and other inexpensive goodies). I suggest saving up and buying the diamond sword and shield, rather than trying to collect enough diamonds. The area that has diamonds also had a very powerful enemy that can move through walls. It's difficult to survive, even with the next best items.

If you're having trouble collecting ore (pre-diamond), you can build walls to give yourself a safe path through enemies. However, once you have a strong enough sword and shield, an open area is preferable. Foraging and battling enemies is more profitable when you can do it quickly. Post-diamond an open area is the only way to go.

The Confusing Map resets the wilderness below your house, so you can collect more ore. It's quite expensive though, and honestly I think it's not worth using unless you've already explored as low as you can.

The Recall, as you probably expect, teleports you back to your farm. It's reusable and not too expensive, so it's worth buying early.

You need an anvil to make a tinker table

If you have ~3/4 of a chest of food, you can get away with just eating, drinking, and sleeping, so long as you have a

Chickens will still lay eggs in the winter, but you need to keep feeding them.

I didn't write down the growing time for each plant in spring, but I think peas are the most profitable.

Strawberries: $30, repeatable (I recommend using these for food. Berries have less nutrition and can be sold for $50.)
Peas: $235, repeatable
Broccoli: $85, repeatable

Cabbage: $200
Potatoes: $???
Radishes: $60

Tomatoes: $60 repeatable, day 10,13,16,19
Corn: $100 repeatable, day 13,16,19

Onions: $80, day 8
Pumpkins: $200, day 14
Cherries: $220, day 14

Conclusion: Corn is most profitable so long as you plant it on day 1 or 2. Remember these are counted by nights, so if you replant onions on day 8, the second batch will be ready on day 15.

Yams: $75 repeatable, day 8,11,14,17,20
Peppers: $110 repeatable, day 8,15

Carrots: $80, day 8
Mushrooms: $80, day 6
Eggplant: $105, day 10

Conclusion: Yams are most profitable.

Used for feeding cows and sheep. You need one hay per day per animal. It grows every season other than winter and doesn't need watering. You can harvest it every other day with a sickle; just be careful not to cut it when it's short. Seeds are expensive and can't be foraged.

Animals give more consistent profits than farming, though it's debatable whether or not they're worth the time. If you have an animal for a long time, it can start producing better goods.

A cow produces small, medium, large, then gold milk. These can be sold for $100,$150,$200, and $300 respectively. It takes around a year of daily feeding and grooming to reach gold. Additionally, after a while, you can give a cow a pregnancy potion. It'll stop producing milk for a while, and you'll eventually get a calf. The calf takes another while to grow to a full cow. It may or may not be worth doing this rather than just buying another cow, but you do get to see a baby cow.

I didn't use sheep or chickens for most of the game, but they produce similar, less profitable tiers of goods.

You need 8 mythril to make a mythril anvil. You can use it with more mythril to make a set of mythril equipment, including farming tools. I haven't gotten any of these items, since it would take a lot of time to get enough mythril. It's slow going traveling multiple screens down from the farm day after day, even if they're cleared out. Each later screen has maybe a couple mythril, so in the end I had to clear 5 or 6 screens just to get enough for the anvil.

The confusing map is a bit of a trade-off. It means not having to traverse as many of the later screens, but also having to remake a quick path through earlier screens. Eventually it would be worth it.

If you're trying to get a set of mythril gear, I'd recommend taking a season off from farming and not trying to go back to the farm every day (use the feeding service if you have animals). Be sure to have a full set of diamond gear and the largest backpack. Also, don't attempt it during winter: That's the only season the sickness bar is really an issue. It also doesn't produce berries, so you'd have to rely on meat and a stockpile of other foods.