I'd max Q. At max rank and with 40% CDR, if you hit someone with it it has a cooldown of 2.4 seconds. Then max E. With max CDR, it has a cooldown of 4.2, and the Q combined with the E's slow makes her basically the stickiest champion in the entire game (if there is a stickier champion I can't name them). The Q is best-used for repositioning in a fight to let you reach a harder to hit vital, I think. W should be maxed last IMO, since it no longer gives free AD.
I'm not sure how to build her though. I tried out a build of Blade of the Ruined King (got it based on the same logic Vayne does), Ionian boots, Black Cleaver (these last two gave me 40% CDR when combined with Sorcery), Ravenous Hydra, Last Whisper, and Infinity Edge (the tooltip on her E after purchasing it clarifies that your free crit does indeed do 250% damage). On your E, this build gives you a guaranteed crit with 1,100+ damage, more if you hit a vital, and you can basically four shot a heavy bruiser while using your ult. BotRK also increases your sticking power even more. Ravenous Hydra was mostly necessary for the waveclear.
I haven't used her in a normal game yet, and I fear this particular build's biggest drawback will be that she's frankly sort of frail. Fiora doesn't have the survivability in her kit that Tryndamere does.