What you might want to consider before buing the armor and in what order you should buy the armor you must first look at your opponents. Are they a majority of attack damage champions or ability power? and also, with the skull sceptre, it gives bonuses to allies around you but it doesnt stack so maybe you would like to consider buying another defensive item against ability power, should one of your teammates have one already.

The healing spell is not just a great spell for defence but also a very good spell against gready opponents such as tower divers. So i really recommend using it, i have gotten many first bloods due to this spell.

Exhaust is also a great spell for both defence and offence. It is obviously great offensively as it slows your target making it easy to catch up and go for the kill. But it is also a great spell for escaping as it then slows the opponent chasing you and might just give you the right amount of time to escape.

A great way of farming with Katarina is by using bouncing blades when you see a couple of minions with low health. This is also good if your opponents are using ranged attacks making it harder for them to harass you whilst farming.

Working as a team is very important and its good not to always be the initiator because if your ultimate is interrupted your less likely to score some kills and thereby wont get your cooldowns rapidly restored. Also remember that with this build you are very squishy early game, meaning you are an easy kill should you not be carefull enough.