The storage tank painting is required by several conditions.
Eliminate the first, obvious one, you don't normally paint the stainless steel tank except special circumstances.
The carbon steel tank should be painted on the exterior to withstand the local weather conditions. The type of paint depends on the location where the tank is operating, a typical paint system includes a primer to provide strong adherence of the subsequent paint layers and also to provide the primary corrosion resistance. It could be a high zinc content primer or a suitable epoxy paint (basically inorganic or organic primer). Apply then a suitable intermediate paint if required and a final top coat for corrosion protection, UV protection, etc.
The internal coating paint depends on the fluid stored, the paint supplier will tell you which is the suitable paint and the application method specific for your application. Sometimes you need protection against corrosive fluids, sometimes abrasive resistant paint, perhaps a combination of the corrosion and abrasion resistance.
You really need to talk to the paint supplier for guidance, since you have to request guarantees for the selected paint suitability in your application.