get ready to lose. like a LOT. Katarina is a all round just absolute shitpick honestly speaking and is nothing but a coinflip. she's not supposed to fit into every comp and if you pick her into shit like Nautilus,Soraka or tanks you basically autolose a lot
she has no Utility or CC.
she gets shut down by CC easily.
due to the nature of her kit being too hard to balance and inflicting sum negative funrates in anytime she's good expect to never see buffs ever.
remember you are truly doing yourself ZERO favors by deciding to main this piece of shit champ over something like Kassadin,LeBlanc or Akali. each game you play henceforth will either be a braindead pubstomp or the worse game of your life where you have zero agency every teamfight and just suck all round.
Conq triumph tenacity Coup
Sudden Imp and Ravenous Hunter
Items: rush Gunblade then go into as much pen as possible. Literally all you do is damage so you MUSt maximize it. otherwise you are worthless. Your basic combo will be E>W>Gunblade>Q>R then pick up the second dagger when they try to run.
Rylais is okay and dont be afraid of picking up HP+AD items after finishing your penetration items. Believe it or not Katarina can actually get away with items like MAW,GA or Titanic Hydra even. her AD ratio's are decent enough.
TIPS:shunpo resets AA timer so use that for last hits or extra damage. Gunblade will cancel your Death Lotus for some retarded reason so make sure to use it BEFORE you R, Use can use Dagger+Shunpo to get over thin walls. Highly recommend using smart cast w Indicators for Shunpo if you are new to her. to clear waves use Q on the middle melee minion then jump behind it and W.