You can pick Exhaust if you want to do the "Special" Katarina combo. (Q , E , W "Exhaust" , R)
I highly recommend Ignite and Flash for Midlane.

I highly recommend to take Sinister Steel second , so you can farm easily. Then Max Shunpo , You need it in Mid game so you can jump at enemies.

I suggest You to take Luden's Echo first, It deals a lot demage. Next take Liandry's Torment so You can be more tanky and not been taken down easily. Take Zhonya's Hourglass for more demage and protecting yourself in teamfights. Finish with Rylai's Crystal Scepter and win the game.

Be careful against Annie , Malzahar , Yorick , Yasuo and Talon. They are very powerful champions against Katarina.