There is no perfect plan. Each fits the bill for a situation.
This plan aims to build stamina and healthy connective tissue and joints.
Do this once each morning and don’t confine yourself to pull ups.
We begin with doing 4 pull ups where we inhale on the upwards motion and exhale on the downward motion.
Next we progress to talking a full relaxed inhale and an exhale on both the upward and downward parts of each motion.
Now we add an inhale and an exhale to each part of the motion once we feel comfortable with the current pace and add a few breaths in between if need be. Mind to count the rest breaths if needed and keep them consistent or lowering in numbers.
Once you can do 4 consecutive pull ups with 10 relaxed breaths going up and the same going down, you will have a better foundation of connective tissue and lasting strength in your upper body and again, do this in the appropriate numbers for other movements such as the squat, pushup and the bridge.