League of Legends (LoL) Question: what is the best jg champion?

There is no such thing as a best jungle champion, but as @thetacoboysaid, Graves, Rek'Sai, Gragas, Elise and Lee Sin are dominant in the current meta. The only champion that I would add to that list is Nidalee, as although she recently got nerfed, (all autoattack resets were removed) she has remained a strong pick in several situations.

All of the abovementioned champions require patience to master, so instead of buying them all and trying to play all of them try to see which suits your general playstyle the most. For example, if you're looking for an assassin champion, Nidalee and Shaco will suit your need, or if you prefer to engage and peel for your team, Gragas and Rek'Sai will do the job.

From stats and experiences, Graves, Rek'sai, Gragas, Elise, and Lee Sin. This is for higher Elo, gold+. For lower, I'd go with something a lot more solo carry heavy, I.E. Master Yi, Warwick, or even Shaco, if you can dedicate yourself to mastering him.

Damage wise ill have to say Xin Zhoa or Master Yi, i prefer going Attack Speed and AD Armor Penn with them, high bursts of Damage is very short amount of time, Tank wise Amumu, Shen (If you know how to go about with him), Warwick (Though he's good with dmg to On Hit AD Tank WW is OP), and Zac, all of them are very simple champs that can carry in solo Ques or give whats needed to let someone else carry but this is also low elo picks. i can go about with builds but thats a whole other note.

Rek'Sai
*She is taken in nearly every "esports game" currently and has an easy kit.

Reksai tunnels and unburrows are broken

elise is a really good champ to hard carry

RENGAR

twisted fate, amumu, udyr, jax, etc.

Volibear is a very strong pick atm!

Zac :) only zac

yi is easy just pull up a build guide right click and boom your as good as a master

Master Yi. Easy and useful. Just go R-E-Q and auto. Build full crit and see what happens.