Item build is made for Katarina to explode her AD power. I usually start with Doran's Shield, to get some life on early game, so its more easy to hunt your enemies if you take de mid-lane.
-The heal Potion can be used if you play offensive. Otherwise, you might not buy it and save some money. I try to play off so I can easily get first blood because the enemies at mid-lane are sometimes squishy heroes
-Sorcerer's shoes / Boots of Mobility. I always choose the first one, because my blades are more efficient with magic penetration since these have magic damage.
-Rylai's scepter. I usually take this item, so my enemies have no scape since my rune build is made for cd's decrease and I get more life because at late game Doran's shield is useless
-Finally The bloodthirster. I take this items because for me its the more efficient when you want to make a full AD hero. Katarina doesn't need critical damage so Infinity Edge is useless too, a complete BT gets +100 Damage, against +80 from IE. Completing your build with 4 BT you would get +400 damage, so your Death Lotus will get more than +500 attack power per blade
My Skill Build is made for a full offensive play, since Killer Insticts just add a bonus magic. Thats why I level it from lvl 17. I gave a level at lvl 7 to get a magic bonus because at that level I wont have much AD. But then, for me, it's useless.
Mastery Tree , as you can see, is FULL offensive too. In early game i will need more critical damage, because I wont make much more damage that the one I have from the beginning.
Try it, and good luck mates!