Hi, I'm Standecni. I'm a Silver III player on the Oceania server. I'm nobody of significance, just an enthusiastic Katarina player. I started playing League of Legends around mid-season 4 and was quite pathetic at the game (that's putting it mildly). After a few periods of not playing, I came back for a while and really started to enjoy the game. Katarina was the first champion I decided to actively main and I haven't stopped maining her since.
The default skill to max first is your Q. This will increase the damage that your poke does and it will reduce the cooldown of the skill as well. Max your W second, it gives you some nice waveclear and it does some nice damage when proc'ing the Q mark. Max your E last since there isn't much to offer other than the cooldown, W will do more damage on a lower cooldown. Of course, take a point into your ult whenever you can. You could took E at level 2 if you need it to juke skillshots that the enemy laner is throwing. Only max your E before W when there are a lot of teamfights, such as in an ARAM, and even then, max them evenly.