My apartment has hot water baseboard heat that is controlled by a zone valve connected to a t-stat. The exterior walls of the apartment are poorly insulated. On the really cold and windy nights we have to keep the heat up all the way to battle the outside temps. We all wake up with sore throats and stuffed up noses. I have done some research and learned that the ideal indoor humidity level is between 30% and 50%. According to the digital gauge I have, we are at 16%, so I think we need a humidifier. It's a 2 bedroom apartment, my wife has asthma and we have a 5 year old and a 3 year old. Any suggestions on what type of humidifier is right for us? Cool mist? Warm mist? Small? Large?

You will have to use a stand alone humidifier. There called console models and many different types of stores sell them. You will have to add the water manually every time it is empty and service the unit once a year.