When starting a factor tree for a composite number does it matter which factor pair you start with and why?

No. Consider 36. You could start with 9 and 4, which would then break down to 3 x 3 and 2 x 2. You could start with 6 and 6, which would then break down to 3 x 2 and 3 x 2. Either way, you're going to end up with two twos and two threes. The prime factorization of 36 is 2 x 2 x 3 x 3.