Alistar is an amazing jungler but I have trouble stealing dragon or counterjungling with him as the game progresses. He is amazing for lvl 2 ganks and beyond with the whole headbutt and pulverize, combo or not.
Mundo is a great jungler but in the beginning (or without the proper runes) you’re going to kill yourself. Once you get used to it, he can do everything. He’s basically a better shyvana.
Amumu is also good, but extremely predictable. The enemy team will KNOW that you’re going for blue asap since he relies on his W. If you have to jungle slower, so be it. His ganks are nice, but they can be minion blocked and are skillshot oriented. Once he hits lvl 6, it doesn’t matter since it’s extremely powerful.
Nunu is pretty nice for the whole learning thing because he has great sustain, simple ganks, and can counterjungle so long as minions are available. He’s not zomgwtfamazing, but he gets the job done.
Master Yi is a bit iffy for me since he’ll either snowball into a death machine or he’ll fall behind and become useless.
Those are the 1350 and lower champs I can think of off the top of my head. Depending on what kind of jungling your team needs or you want to learn, you should learn a few junglers. There are some junglers who can gank without their teammates’ help (Mundo, Lee Sin, Nocturne), some who set things up (Alistar, Nunu, Nautilus), some who clear fast enough for stealing/counterjungling (Skarner,Udyr, Shyvana), some who just simply do everything (Lee Sin, Udyr, Skarner, Mundo).
Warwick does not jungle quickly, he jungles consistently. If you want to see a fast jungler, go see skarner, mundo, shyv, or just about anyone with spammable aoe abilities.
In the end your job is to make sure you have a strong early-mid game and that your lanes who are getting countered/beaten on farm have a little ace in the hole. Choose your jungler based on team comp and skill because laning phase is not everything (if you guys don’t have a tank or have no form of CC you’re going to have trouble unless you wtfpwn them early). You don’t want to pick someone like Shyvana who is mainly for stealing jungle creeps/dueling junglers if you’re playing with people who need ganks, aka 80% of the pub players. You don’t want to pick a jungler who sets up kills if your top/mid are tanks who cannot do enough damage to get a gank off if you come in. You don’t want to be a solo kill jungler if you plan on stealing kills from your ad carry. Once you have a good roster/understanding of jungling then you will be the one to control the game. At the start it will look like clearing camps and ganking here and there but to be a badass jungler, you’ll have to look into ward placement, communicating with CVs, jungling match-ups, uncommon ganking areas, and coordination with your teammates to find out where the enemy team has placed wards. After you learn all that crap you can control games.
FYI it doesn’t matter how awesome you are at jungling if there are certain situations like top lane and bot lane are both feeding/dying a lot. If you don’t correctly balance your time between camps and ganking then you will fall behind and become useless. You will get a lot of hate since it’s easy to blame the jungler (hence the recurring joke).