I would recommend to start with (w) sinister steel, I'm not crazy. This is a choice I take because of short cooldown and larger area farm. If you are standing in a cluster with many minions with a small amount of health you will definitely get a great big chans of getting all the last hits. Starting whit the W is also a god choice if your team is gonna start an invade.

I don't use Doran's ring because katarina has no mana cost, and you use amplifying tome (the book) to build death fire grasp.

I don't want to be a teaching League of Legends Nazi, so feel free and try out what is the best build for you. But when you have finished your build it should look something a little bit like this

Death fire grasp is the most important item in the hold build (my opinion). I like to have death fire grasp on the button "2" so the passive is easy to use in a little stressing situation, or in a situation that you have to think fast.

This is my first build, hope you like!

P.S when you have reatched your finale build fantasy, buy tons of Elixirs!!!!!