What are the best and easiest food/elixirs for stamina increase?

While cooking 5 extra-stamina-wheel foods can be good if you want to burn through multiple wheels of stamina all at once (such as slow-time arrow shooting or very long glides), if you're going to be doing activities where you can stop and eat food halfway (such as climbing), the most efficient way to restore your stamina is to cook a single one of these ingredients by themselves, as any food that increases the maximum of your health or stamina (even if just by a little bit) will also fully replenish it.

With this in mind, while 5 Stamella Shrooms in a pot will give you two bonus stamina wheels (and will fully recover your normal stamina, effectively giving you three worth), if you cook each one individually and then eat it just as your stamina is about to run out, you can effectively get 5 or so stamina wheel's worth. If you've buffed your maximum stamina amount at all, the difference can get even greater.

Take a look at this Quora article. They list the top 5 things that can be used to help with stamina. The first one on the list is Endura carrots. I would say this qualifies as your best/easiest thing to obtain. They can be found in Karkariko village (which I know you've already been too), and "cooking 5 of them in a pot will give you full stamina recovery and 2 extra wheels".

Here is the full list of the article:

1. The Endura carrots are great. Cooking 5 in a cooking pot will yield a full stamina recovery and 2 extra stamina wheels (they are golden). this works especially great when you are, for instance, in the Hebra mountains, or the Gerudo Highlands, when you are climbing lots of mountains and steep cliffs.
2. The Stamella shrooms work great, too. I believe cooking 5 in a cooking pot gives you 2 whole stamina wheels.
3. Staminoka Bass are good. This will give you at least 5 hearts and 2 or 3 wheels of stamina recovery if you cook 5 in a cooking pot.
4. The restless crickets don't yield much recovery, though. Cooking 4 restless crickets with one monster part (bokobolin horn, moblin guts, etc.) will give you one or 1 and a half stamina wheel recovery.
5. The tireless frog will give you extra stamina wheels. I think 4 tireless frogs with 1 monster part is full stamina recovery with 1 extra wheel.