Neither, the type of move does not affect the speed at which it is used. Physical, Special and Status moves all depend on the user's speed, so none of them goes first or last.
If your opponent is going first, then he simply has to have more speed than you. Maybe he has a speed boost or you have a speed drop, or he's using an item like Choice Scarf. Or he could be using a priority move, like Aqua Jet or Bullet Punch. There's also the possibility of Trick Room, where the slower Pokemon moves first.
Hope I helped!