The best picks not in lane to counter Twitch include Naafiri, Sejuani, and Elise. These picks are all great at countering Twitch with decent win rates over 58%. Even if these Twitch counter picks are not chosen opposite your position, it's not a good idea to choose him into these matchups. They will likely destroy Twitch.
Yet, if the opposite team picks either Galio or Rumble, you should strongly consider taking him, as he easily crushes these champions with win rates over 55% against both ofthem.