torque - Newtonian Mechanics - How does something like a car wheel roll?

Ok so please bear with me here and what is almost certainly a really stupid question, partly because I don't quite know how to ask it.

When you have a wheel such as one attached to a car, a torque is applied to it from the engine. It's my understanding that the wheel would slide over the road and the car would not move if it were not for static friction which is of course the concept of rolling without slipping.

The problems I am having is when I consider what the magnitude of the force exerted on the road from the wheel would be, or specifically the equal and opposite force exerted back onto the wheel from the road via static friction. The reason for this is because I want to say that it is just the torque exerted on the wheel by the engine divided by the radius of the wheel but that seems to lead to a ridiculous conclusion. If I follow that logic, then the equal and opposite force exerted on the wheel by the road, multiplied by the radius of the wheel to get the counter-torque, is equal to the torque exerted on the wheel by the engine but in the opposite direction. That of course would mean that there is no net torque and the wheels would never move (unless the force were greater than that available from static friction but then it would just slip) which means that the car would never be able to move! So simply put, what am I missing that is almost certainly staring me in the face (again)? Clearly things roll and cars move so I know i'm going horribly and embarrassingly wrong somewhere.

Also, I often hear people say that static friction is the force responsible for propelling a car forward. How is that the case when it acts in the direction opposite to the direction that the wheels are trying to roll? That's sort of the same question but I think it may help highlight my misunderstandings of rotational motion in this area.

I never knew wheels could be so complicated! At least for me anyway.