For nice weather and smoother roads, where you want to go fast, the road bike is the ideal tool for the job. For rough roads and off road, the MTB is a better tool. For commuting, the ideal is a commuting bike, this would be a hybrid or cross style bike with internal gear hub (possibly even belt drive), fenders, chain guard, rack and puncture resistant tires. For touring the ideal is actually the mountain bike, with road bars, plus the racks and fenders. Bicycles are inexpensive enough, that we can treat them like a tool. Unlike a motor vehicle, where you often need to compromise.