A 28-year-old woman with type 1 diabetes presents to the emergency department with 24 hours of polyuria, vomiting and abdominal pain. Her capillary glucose is 26 mmol/L; venous blood gas shows pH 7.14, bicarbonate 10 mmol/L and marked ketonaemia. She is tachycardic and dehydrated but haemodynamically stable. After initial assessment, which is the most appropriate immediate management sequence?