The choice of media should be cell type and application dependent. Typically, growth media is required for cell expansion prior to seeding on permeable supports and for cell growth on permeable supports. When an optimal cell confluence is reached on the permeable supports, differentiation media in the basolateral chamber is required to achieve ALI. There are commercially available media for cell expansion and ALI culture. For example PneumaCult-Ex Medium Serum- and BPE-free medium for expansion of primary human airway epithelial cells , PneumaCult-ALI Medium Serum- and BPE-free medium for human airway epithelial cells cultured at the air-liquid interface, as well as supplements such as Hydrocortisone, are all available from StemCell Technologies. Scientists at Corning have experience in culturing primary airway epithelial cells for ALI model establishment using Pneumacult media with supplements Hydrocortisone and Heparin added to the medium and it has been effective during the process.
If you are working with stem cells (eg. iPSCs, organoids) you will need to include ROCK inhibitor in the culture media during permeable supports seeding as you would for single cell passaging. For specific cell types of interest literature available on the web would be a good resource for specific media component requirements.