Rush abyssal if you're against AP champs and zhonyas if you're against AD champs. After that you usually want to get sorc boots unless you feel you can purchase another large rod before getting the boots.
If your team is ahead of the enemy team by a lot, deathcap is the better way to go as raw ap is usually the better stat for katarina. The only times I would get items like Liandry's + Rylais before deathcap would be if the enemy team has a lot of mr on their team and I need some way to bypass the mr plus the slow from rylais is quite nice. After that you can just get a void staff.
So basically
-Little mr on enemy team = Raw AP
-More mr on enemy team = Mpen items for tankiness and cutting through the squishies and tanks.

I'll often replace the rylais with void staff + abyssal scepter against ap's unless I feel like pissing off the enemy team with the slows from rylais because who doesn't love being slowed down while facing kat's combo
Plus, glass Kata is more fun in my opinion then mpen Kata so I'm a bit biased towards glass Kata.
By mid-late game, if you have enough money, get the ap elixir for the extra ap whenever possible. it's quite helpful in case you can't afford the ap items you need.
Hope this helps.
Also, am I the only one who likes to place the items in a certain order in the item slots based on the value of the item???
Ex. from slot 1-6: Deathcap, Zhonyas, Ludens, Rylais, Void Staff, Sorc Boots