By far the most accessible option I found after a decent internet search was the ridiculously huge apple orchard you find on Satori Mountain, east of Central Hyrule, right next to Sonapan Shrine. A full harvest will give you about 150 apples & a few golden apples. If you cook all of these into meals (5 apples together) you can make a bunch selling them. Keep the console powered on next to you for about half an hour and they will all respawn and you can just do it over and over. And you never have to worry about having enough food!

Bonus tip: Farm arrows from the Battle Talus outside Saharsa Slope Skyview Tower southeast of the castle.

Bonus bonus tip: Chopping grass with your weapon anywhere in Hyrule Field has a decent chance of getting you a Restless Cricket. Cook four of them with a monster part of your choice for a full stamina circle elixir.

I haven't found a need to farm anything other than the above so far.

If you feel like glitching, dupe diamonds. The shield hop dupe glitch will let you dupe 5 at a time.

It made me a bit nostalgic for the Elder Scrolls method of having each merchant having only so much money to buy from you with, which limits tricks like that. I'm dubious that Beedle really had 5000 rupees for me.

Just play the game— find, make, and sell stuff. It’s a really fun and well balanced experience as-is IMO, go do other thing if current thing not doable.

Check every cave, harvest ore, take the stonez to the Gerudo Woman in Goron city to get 10% more.

Dupe diamonds, profit.

The IMHO easiest way to make a bit of extra cash is to cook stuff you already own before selling - it might not be "get super rich super fast" useful, but requires basically no effort. In BotW, a meal or elixir made with 5 items sells for approximately 2.8 times the value of all raw ingredients combined, so you basically get thrice as much cash just by tossing stuff into a pot. I haven't checked the multiplier in TotK yet, but stuff still gets "more valuable" if you simply spend a couple of seconds at a cooking pot, and the new recipe selection thing makes it faster than having to manually pick items from your inventory every time.

Personally, I also sell Luminous Ore. There are plenty of ore deposits all across Hyrule and since I don't like the one armor set they're needed for, I always end up with a surplus. You can also feed them to Dondons and they might poop out more valuable gemstones sometime later, but I don't like to gamble and rather just sell the L.Ore directly.

Oh and Fire & Ice Wizzrobes are easy prey as well, as they die to a single hit of the opposing element - toss a Fire Fruit at a Blizzrobe and it will go poof immediatly. You can then pick up their "rods", travel to Tarrey Town, pay the Goron kid 20 rupees to take the thing apart, and you will get a ruby or sapphire each time. Works with electro Wizzrobes as well (Topaz) but they're not as easily OHKO'ed as their brethren.

Make elixirs. The sum of the item prices you use in the elixir x1.8 will be the sell price.

The other thing is for early on in the game, just sell star fragments and diamonds. You will get plenty more over your 250hrs + journey. Or if you are like me, I just keep 10ish of things like rubies in my inventory and sell excess, until I have a reason to collect them (armour upgrades).

Molduga's are easy to hit up, same with Talus, and they will get you some good parts for elixirs. Just bare in mind drop rates of some things (Molduga jaw are rare for example but guts and fins come in plenty. Similarly Lynel guts are rare, but other parts are plentiful. (You probably are not planning to hit Lynels yet though)

Well the best way I've found is just killing the taluses, a lot like BOTW. Either look up their locations or get searching, kill a few every blood moon and you'll be doing fine.

Beyond that, monsters drop way more monster parts in general for this game, sell elixirs. If you do this, be aware that sell price is based on ingredients, not effects, and there's a money multiplier for more ingredients, so cooking 5 at a time is always better, although you might wanna look online for the most valuable parts. Generally, rarer the better.

Another way is to check your game version and use whatever dupe works for that version, there's a few, but not everyone wants to do that.

I just sell stones and things I have in large quantity. I also heard that cooking skewers of five prime meats gives a good return. Prime meat is plentiful in Hebra if you hunt wolves and moose.

Explore every cave you come across and get all the ore. Sell gems and lower level monster parts at every opportunity. Resist the urge to hoard stuff, especially in early game. Soon enough you will be able to save up lots of money!