Final answer:
The most crucial equipment to have at a client's bedside after a subtotal thyroidectomy is a tracheostomy set, due to potential airway complications.
Step-by-step explanation:
After a subtotal thyroidectomy, the most important piece of equipment to keep at the client's bedside is a tracheostomy set. This is critical due to the risk of airway obstruction post-surgery, which can result from swelling or hemorrhage. A tracheostomy set allows for immediate access to emergency airway equipment should the patient develop respiratory distress and require an alternative breathing passage.