WEAPONS
Here are a few videos on weapon locations that respawn after a blood moon:
If you want a list of Top 10 weapons, here you go as well:
ARMOR
As for armor, you want to get the temperature resistant pieces, like in Rito Village to resist cold weather, Vai/Voe clothing in the Gerudo Region, and Flamebreaker armor in the Goron region up at Death Mountain. The Zora armor helps with swim speed, swimming up rivers, and spin attacking in water, but that's mainly necessary to have for a quest(s). I rarely use the armor from the Zora Domain.
I don't know much about shields, because I mainly use the Hylian shield once I got it. It costs I think 4,000 rupees to buy a new one from a person in a secret town, but I can easily make that kind of cash with the Snow Bowling game. Doesn't even take that long to make 3,000 rupees with the game once you get the hang of the sweetspot.
FOOD
You may not realize it, but cooking food DOES matter when it comes to dealing with the boss fights and such, because some of them are quite difficult. I mean you can survive without food but you have to play really, really carefully. You can get some easy meat by playing a hunting game over and over, but animals aren't uncommon to find in forest/woods areas. What I do recommend is going to the Snowfield Stable, and wander around the field of the stable. You'll find Snow Elks, Wolves, Foxes, Rhinoes, and maybe a few boars to kill for meat. There is a good amount of animals there with good quality meat, so wear your warmest clothes and get a bow with some arrows to do some old fashioned hunting.
TO BE CONTINUED... ( I will edit this later, I have somewhere to be. Reply to this post so I know when to come back
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