Lately I've been talking to my challenger friend who plays Katarina here and there and is very good with her. As a Katarina main I would always shy away from Hextech Gunblade when DFG was around because it was clearly the better option. Now Hextech Gunblade offers more AP, good flat damage with it's active and overall good stats including the lifesteal and spellvamp. It's an item that is extremely viable on Katarina right now. I hate it when players say that Katarina doesn't benefit from the spellvamp and lifesteal because she really does. The amount of times I've gotten a reset and been hugging onto my E and Q for spellvamp to keep me alive is ridiculous. To conclude I highly recommend Hextech Gunblade so far as to say it is one of Katarina's core items.

The defensive items
Banshees and GA can be items that you can build mid-game if you're extremely fed and want to be up in a carries face auto attacking them - but as for late-game they're items that can keep you alive and allow you to benefit from an assisted reset.

The aggressive items
Mejais... Oh you guys that love to build this item. I wouldn't say it's a good choice since once you get 20 stacks and die, you lose half of them. But if you're feeling unkillable - go ahead Faker.
Rylais. A good item but I generally wouldn't build it because of the other item choices there are. It is a very good item though as it offers 100 AP and 400 health along with the slowing effect on its passive.

Cons
I wouldn't necessarily give Katarina too many thumbs down since she's the only champion I play lol but the only downside to her can be lockdown.
NOT CC but lockdown.
By lockdown I mean - dedicated abilities that can completely disable Katarina. Examples are: Malzahar ult. Annie full combo. Warwick Ult.
Don't get me wrong though it isn't the end of the world unless that Malzahar, Annie or Warwick are fed. It can easily be avoided ^^

Pros
I'd like to mention that her new auto attacks are amazing and that it helps her a lot through laning phase against champions like Syndra and Ahri who will punish you for taking too long to auto attack a creep.
There's also her insane output of damage.
Her incredible resets.
Ward jumping.
The speed buff you get from your W once you hit an enemy champion with it.
There are soo many to list but the best thing about Katarina would have to be her roaming. This champion by far has one of the best roaming potentials in the game due to her resets and mobility with her E.

Never blame your team.

As Katarina if you are in a stage of the game where the odds of either enemy team winning is 50/50. YOU CHANGE THOSE ODDS TO 100/0.

The moment you see a kill, go in there and do everything you can to assassinate them and E right back out the moment they die. Right after you assassinate someone your team should go full engage in and you should be able to follow in and win the game.

Team-work is important but when you're playing Katarina and solo queue in general with any champ - play for yourself and do as much as you can to aid your team to victory.