For most purposes, you will always use Integer, a signed integer type which has the “natural” size of such types for the machine. On most machines GPC runs on, this is a size of 32 bits, so Integer usually has a range of -2147483648..2147483647 (see Integer).
If you need an unsigned integer type, the “natural” choice is Cardinal, also called Word. Like Integer, it has 32 bits on most machines and thus a range of 0..4294967295 (see Cardinal, Word).
These natural integer types should be your first choice for best performance. For instance on an IA32 CPU operations with Integer usually work faster than operations with shorter integer types like ShortInt or ByteInt (see below).