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.
He loses 6 armor from scaling and 4 at start. 10 armor lategame won't be noticeable. The 4 armor make a difference on first clear and in duels. I don't think that makes a big difference at all.
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,
*She is taken in nearly every "esports game" currently and has an easy kit.