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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 section 9.125 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 section 9.37 Cardinal, section 9.303 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).