This is more of a build than a guide, but there will be small parts like the Pros/Cons bellow.

Pros.
No Mana
Low Cooldowns (especialy with runes mastries, and boots.)
Good escape (shunpo)
Gtear Ganker and Chaser
Easy Mode
3 target Ult

Cons.
Can be foccused like crazy
Bad early game farm
CC interupts ult.

Doran's Shield over Boots?
I find that the Doran's Shield coupled with the defensive masteries gives Kat great lane sustainability. I also find that Boots on Kat early is unnecessary because of her easy escape with Shunpo and the sustainability with Doran's Shield.

The next item i get is Hextech Revolver. This is a fairly cheap item that is great for Kat, giving her some much needed AP for some early damage, and spell vamp to help with more sustain.

Now on to boots.
Ionian Boots of Lucidity or Sorcerer's Shoes?

This is another change I have to other builds.
Sorcerer's Shoes can give you some Magic pen, sure. But the cooldown reduction from Ionian Boots of Lucidity I find is way more helpful in giving an edge over the opponent (Quick Shunpo is your friend ;).
Also, because of the Void Staff later in my build, you wont need the MP from Sorcerer's Shoes.

Next item i like to get is Rylai's Crystal Scepter