Looking at this current emergency as a guide, where many people will need to shelter in place and avoid intersecting with the medical system until they have objectively reached the point where they require invasive supportive care, it’s imperative that every family be able monitor and record a sick patient’s vital signs.
Temperature - requires thermometer, can use industrial instruments like thermocouple/multimeter or infrared gun.
Blood Pressure - requires a cuff, the automatic kind don’t require training or a stethoscope.
Pulse Rate - requires counting pulse for one minute, also typically provided on automatic BP and Pulse Ox devices.
Respiratory Rate - requires counting breaths for one minute.
Oxygen Saturation - requires measuring how much of the blood’s oxygen carrying capacity is being utilized.
Obtaining this data and writing it down several times a day provides a lot of useful information on how a patient is managing the infection over time.
If you don’t have all this equipment you can still measure pulse and respirations with a watch and subjectively assess how hot they feel to the touch. Bluish lips and fingernails indicate critically low O2 sats. Lightheadedness when sitting or standing indicates low BP.