If you only ever do 1 pranayama exercise, the complete breath would be the best. You can start with it, or just do it at the end of class, as the pranayama. Or before other pranayamas, also at the end of class.
There are many ways to do & teach this. I first learnt it, over 40 years ago, from Dr Swami Gitananda. He divided the lungs into left & right lobes....& this is how they are, physiologically. Then into lower, mid & upper sections. In the left lobe area, the heart takes up a fair bit of space, but still he recommended to stick with the 2 lobes, & 3 sections, plus front, back, & sides. This was for pranayama reasons, and also lung health. There are networks of nerves in the front & in the back of the lungs. And, as we know, nerve impulses carry messages to & from other parts of our physiological being. To build up nerve health is also to build up our nervous system so that we are then able to decrease, without any effort, our over-sensitivity, & in this way we can become calmer & more balanced.
Dr Swami Gitananda taught the use of hand placement on the front, sides, & back of the chest. Leading up to the Complete Breath. The Complete Breath is a deeper & longer breath than what we normally use. From here, he introduced hand mudras for the upper, mid & lower lobes, & also for the Complete Breath. All of this is very profound. I learnt all of the hand positions & mudras with the breathing practices & diligently practised them. It all taught me the power of deep breathing. How it definitely gives one more physical energy, more mental energy, & the transformative power on one's consciousness & prana levels too.
Later, I lived in an ashram, where we were taught to breathe deeply, it was breathing deep so that one's belly moved, then adding the breath travelling up the lungs. I did not find this so effective, but this was supposedly the official complete breath of the time, so I taught it. Later adding one hand on the upper abdominals, 1 hand on the centre of the chest, as the breath will go to under hand placements. Quite a few years later, the same ashram added hand mudras for breathing, using the 3 lobe areas: lower, mid, upper. The thing is, our lungs are not just flat "things", they have depth & width, lots of tubes for the air to move in. They are complex, & I do not feel that, except for Swami Gitananda, & now Dr Ananda, his son (successor, at Ananda Ashram, Pondicherry) , that this has been properly understood.
We can get around this, without using hand placements, by how we describe the complete breath. This is my channelled version, & it is very effective. Try it & see:
Breathe into the base of the lungs, as though they form a tyre inner tube, & you are breathing into this tube, filling it up. Like an expansive front, back, & sides movement. Do this a few times. Progress to doing this & continuing the breath up through the chest to under the shoulders, as though you are breathing up a wide column & filling it up, front, sides, back, middle. Pull the abdominals in slowly, as the lungs deflate. Our lungs don't go up to the shoulders, & but, in order to get the breath up into the top peaks of the lungs, this is a good visualisation to use. This technique also leads nicely into adding ujjayi.