Viable offensive items
Not Updated For Current Season
While Katarina jungle is a weird pick and quite overlooked, she is actually a solid pick. Her early clears are weak, but that doesn't stop her from becoming a monster mid and late game. Another good thing thing about Katarina jungle is that it allows for an AD build and highlights it's strenght.
Creeping / Jungling
You should always start with krugs. If done correctly, you will be able to survive clearing red with a small amount of health. After you finish that, you can either recall or try getting the scuttle crab. Getting the scuttle crab is risky because it can lead to you encountering the enemy jungler, but if that doesn't happen, clearing the scuttle will give you enough health to clear 1-2 more camps. After that you should get a couple more pots to sustain yourself, but clearing the jungle becomes much easier.
The mastery page shown is mostly revolving around increasing your survivability and damage you deal to jungle monsters.
In both AP and AD build your w, Sinister Steel is the first ability to take, mainly for it's low cooldown and damage. In the AP build you are choosing between maxing out your w and q, although I personally prefer w. In the AD build, you always max w first, since it scales off of AD.