In VB6 it was indeed best to use a Long, because due to the 32-bit architecture of the OS, it is more efficient; however, VB6 is an oddball, because C++ and other languages have always had 32-bit ints.
In .NET you should stick with Integers. If it confuses you, the standard types (Integer, Long) are just aliases of less confusingly named types; Int16 is 16-bit (Short), Int32 is 32-bit (Integer), Int64 is 64-bit (Long). They can be used instead if it is more comfortable.