This guide is aimed at newer players. The natures have been sourced from pikalytics.com, smogon.com and a proportion have been checked with cantsay.github.io Pokémon LGPE calculator at level 50.
Please remember there is not always a *best* nature. It is purely how you select, build and plan your team. Please be respectful to the OP and each other in the comments.
** N.B. Most of the document's data was hand collected and written. And therefore, subject to inaccuracies.
*** Finally, would love your ideas for comments beside each Pokémon. To enter a valid suggestion please limit your idea to the size of the box in the document or as small as possible; to suit the mobile phone users and tag me @Ravakahr. I will search CTRL + F for your ideas :).
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*****Advanced players, special note for you.... * even though this guide is aimed at newer players so they can mass catch Pokémon more easily, and have a great stepping stone into competitive battling; when using this guide, you will still need to damage calculate each Pokémon for yourself and build specifically for your own team. I cannot make this any clearer. A lot of the current calculations have been based on a lgpe calculator at level 50 and meta analytics. The best example is eevee. A smogon guide suggests jolly. The meta is using 61% jolly. The same Smogon guide suggests Jolly is great to out speed venusaur and dragonite. However, both those Pokémon 2hko eevee. In fact, dragonite can 1hko with stealth rocks. So why are you going Jolly nature to out speed a neutral speed natured Dragonite? What if the Dragonite is a mixed/special attacker? Burn won't have much effect? Eevee is not used to sweep but as a cleric to remove team status and apply status (burn/para etc).
The calculations (skip to summary if you need) Muk-A can 2hko eevee, whereas eevee can 3HKo Muk-A. If you were building to battle a muk jolly would not be used. You would use impish and then muk would 3HKO eevee. Same vs Zapdos and mew, both out speed and have a chance to 2HKO eevee. If careful nature was used, it may now be a 3HKO. However, they both out speed eevee. So eevee will only receive 1-2 attacking turns. Finally, are there stealth rocks on the field? Will eevee apply burn status first? etc. etc. etc. You must build purely to your team strengths and what you want to you counter. This is where *there isn't always a best nature* applies. Maybe you want to go Sassy so you don't get an extra turn sleep?
In summary, and in general, if you want to live an extra turn, and when not calculating stealth rocks into account, Careful nature will not help against muk - you need to be impish. If you want to live an extra turn against mew/Zapdos, Impish nature will not help you need to be Careful nature. And finally, Jolly nature won't help you live an extra turn against either of those listed above. Eevee is a great example because it’s so borderline with the natures for survival.