I have spent more time on jungler than any other role besides Ranged AD. As an avid jungler who is trying to take the best jungler for my team, I like to keep a variety of options available. Below are just the basic thought processes of my jungler selection...
If my team has plenty of DPS from our laners, but very little CC, I'll take Maokai so I can be the frontline initiator and protector.
If my team has good DPS and also has some CC, I'll take more of a faster clearing champ with a hard CC like Skarner.
Both of those champions typically start with Regrowth Pendant, use Defensive masteries, and build Gp10 items so they can focus on ganking. They are great initiators and protectors of your team as well, and also deal quite a lot of damage over long fights.
If my team has moderate damage and moderate CC, I'll take a champ like Shyvana. She doesn't have strong CC, but her disruption, aoe DPS, insanely high clearing speeds, and her ability to counter jungle make her a great pick in a fairly balanced team.
If your team needs DPS from their jungler because they have quite a bit of CC and toughness in the lanes, you can go with a more DPS jungler like Nocturne.
Obviously, there are lots of other options out there, but I have found that these 4 really cover a lot of areas and are quite easy to learn and become fairly good at with only about 10 games each. Also, Mao/Skarn run similar runes and the same masteries, as do Shyv/Noct...that helps a lot too, for those of you who maybe don't have tons of rune pages, or are still building them.
Udyr is another great option somewhere between Skarner and Shyvana. But Udyr is so flexible, you can really build him multiple ways. Just depends on your personal preferences.
Check out some of the pro guides for these champs for more detail on how to use them, but I feel like they are some of the most powerful, useful, yet simple/easy champs for jungling in the game. All of them are great for getting started in your jungling career!