For addition codes, you can choose any number. For multiplication codes, your encoding number must have no prime factors in common with the modulus. Otherwise, it will be impossible to decode your message. Note that 13 and 26 both have the prime factor 13. If you use the 26 that is already typed in, you have a 26-hour clock, where 0 is the number after 25.
Addition is on the clock.
So, working backwards through the encoding instructions, here is how to decode. Each number of the encoded message is decoded by subtracting the encoding number you chose. Remember that subtraction is on the clock. If you used a multiplication code, each number gets multiplied by, instead of added to, the encoding number. The inverse operation to multiplication is division, so to decode the message, the recipient has to divide by the decoding number.