There in is the thing, Twitch is one of the last remaining actual hyper carries in the game.
He's rough to start off, but when he hits the 2-3 item point, he can shred a whole team without a ton of effort.
There seems to be 3-4 builds that are common currently for Twitch
Build 1 that C9 Sneaky uses: rush
then build
Lifesteal item, Mercurial then move on from there. Boots inside the build at some point of course.
Build 2: The old standby of BotRK, into a BF item, followed now by hurricane, and other items as you see fit.
Build 3: Ghostblade rush, into hurricane, BF item, then the rest as you see fit.
Build 4: Rush hurricane, into the rest of your damage items as you see fit. IE is usually second in this.
Builds 1 and 3 seem to work the best, 4 is next on the list, followed by the BotRK build being last place as it takes too long to ramp up.
The other issue is that Twitch requires a weird playstyle. You have to balance him as both an ADC as well as an assassin. Add to all of that that the only supports that should be played with twitch are the same deal as the ones played with Kog'maw, ones to keep him safe.
So be careful what you're picking him against, along side, and what you're building. BotRK is a rather archaic build that should probably be shelved for the time being.