League of Legends (LoL) Question: Which champion is the best to learn to counter-jungle with?

Technically all junglers can counter-jungle, and each have their own potentials at counter-jungling. Some of them are worse because they have no escapes or low damage, and some of them are better because they clear quickly or cannot be outdueled.

Since you want to learn counter-jungling, it's best you learn the capabilities on each individual jungler.

However, some good counter-junglers and junglers as a whole to get you started are Shaco, and Lee Sin.

Shaco has a great escape / chase with his Deceive and can easily camp buffs with his boxes ahead of time.

Lee Sin is extremely strong early on because of his many damage abilities and has a relatively easy escape with wards or jumping to allies.

I feel like counterjungling is the easiest way to snowball as a jungler this season. Lee Sin and Shaco are god tier counterjunglers. Vi, Udyr, Shyvana, Hecarim, and Zed are not far behind. Nunu and Cho' Gath are great get in, get out counterjunglers, but they have terrible dueling capabilities, so I consider them "counterfarmers" for lack of a better term. Other less effective yet still very viable counterjunglers are Jax with his amazing dueling capability, Wukong is an above-average duelist and he has a great escape, Darius with his high base movespeed and dmg, and Fiddlesticks can easily lock down the enemy jungler and kill him if he is at relatively low health. Of course counterjungling is risky especially for junglers with a low clear speed. Also, counterjungling isnt only for junglers. When I am playing an assassin at mid, perhaps Talon, Fizz, or Akali, I always ward the enemy wraiths so I can pick up an easy kill if the enemy jungler is doing wraiths at low health.

Nunu and Cho'gath seem to be the best counterjunglers to me, since they have like a double smite, clearing enemy buffs almost instantly.

However, if you are new to counterjungling, you might prefer something more quick, since Nunu and Cho'gath are rather slow champions.

Shaco for example, is maybe a bit slower with the counterjungling itself, but if you are busted, you just Deceive away. Also his boxes allows you to have more vision in the enemy jungle, which also is nice to have.

Embracing also mentioned Lee Sin, although Lee needs a bit more expierence than Shaco.

Tl;dr Pick Shaco, he is the easiest counterjungler.

There are quite a few junglers who excel at counter-jungling, like Shaco, Shyvanna, and Lee Sin for example, but since you have experience with tank junglers I would suggest trying Nunu.

Nunu has incredible clear times in the jungle by starting machete/5 heath pots and utilizing the minion damage and healing from Consume(Q) and the attack/move speed boost from Blood-boil(W). If you can get your team to give you a smite-less blue buff then, against the right jungler, you can go steal their red using Q, W, and smite; instant double buffs and your level 3 while the enemy jungler is only level 2.

Very good counterjunglers in the start is probably champion with high damage and good escape, here's the best counterjunglers in my opinions:

Lee Sin: Nobody takes him in a fight, hes good escaping and high damage
Jax: Can easely jump to friendly wards, very hard to beat in a fight
Shyvana: High mobility with her W, also fast jungler and haves her jump-everywere-ultimate!
Twitch: If you're op enough to play him jungle and you get fed/farmed, you´re the ultimate jungler with over-high damage, stealth and a slow!
Shaco: Can jump away easely, and stack his Jack In The Box to guard!

I can't recommend any other jungler than these and Nunu & Willump + Cho'Gath with their duble smite!
(that have been mentioned before), but since they're so dang slow, dont start jungle with them (counter)!

I would advise you not waste that much time couterjungling this season. Unless you take buffs, it is really not worth it. Unless it is the only thing you can do for some reason. (enemy lanes are playing very safe, and you have vision of enemy jungler)