But the whole thing is stationary, so Newton's 3rd applies to everything! So that doesn't help me: The wheel is pushing on the ground equally and opposite to the Friction force pushing on the wheel, and the wheel is pulling on the bicycle mass equally and opposite to the bicycle mass pulling on the wheel.
What I am trying to do is find the forces acting on the wheel
The wheel is not moving laterally, so the friction force must be opposed equally by the bicycle weight.
The wheel is not rotating, so the torque due to the friction and the weight force must be opposed equally by the torque from the brake? How do you work these out?