Itemization
League of Legends consists of over a hundred different items that may or may not be good depending on the champion, matchup, or game in general. Knowing the standard items that are always generally good, as well as items that should be picked up in niche situations, is essential to properly playing the game. Being in the jungle makes this process a bit easier, while at the same time make it more difficult through the smite item choices.
Items for AD
If you are playing a more AD reliant jungler that plays more as a bruiser than an AD tank, you should into picking up the blue or red smite item, with the AD echantment. However, most AD junglers do not need to rush the completed item, and leaving it alone at the blue or red item alone is sufficient. If your clear speed is low, rush a tiamat, or start building into items such as Trinity Force or Black Cleaver.
Items for AP
AP focused junglers on the other hand should prioritize finishing their Luden's Echo echantment for their jungle item. This gives beneficial stats, as well as immense jungle clear and ganking opportunities with the passive proc. Once this item is completed, a Liandry's or Rylai's are two great next options, or if you need to be a bit tankier for the team, an Abyssal or Zhyona's would be good alternatives.
Other Items
If you're a tank or more of a hybrid jungler, there are many other options for you to try out. Generally, you will be building the Bami's enchantment varient of the jungle item, however, you have the flexibility of possibly going one of the other, damage focused ones and then transition into a more healthy build. Items such as Deadman's, Warmog's, Rylai's and Spirit Visage are all excellent choices for tankier junglers. If you are playing a champion such as Master Yi or Udyr, you may consider picking up the fourth, extremely niche, attack speed jungle enchantment.