To create a custom container class for integers, doubles, and strings, it is essential to consider the programming language being used. In C/C++, it is recommended to define types like INT32 to ensure consistent size across platforms, as the size of standard integers can vary between 32-bit and 64-bit systems. For string handling, the approach depends on whether strings are fixed-length or dynamically allocated on the heap. If using heap allocation, a struct may not suffice for storing string data, and a large flat memory area can be utilized instead. In Java, generics should be employed, utilizing collections such as List<A>, ArrayList<T>, or Vector<T> to manage different data types effectively within the container class.