Does it matter what two factors you select to complete a factor tree? and tell me how you knew

No, just keep factoring until you cannot factor any further.

example:

90
.^
9*10
^^
3*3*2*5

I could also start with 15*6, 3*30 or whatever. but the final answer will still be
2*3*3*5 = 2*3^2*5.

No. as long as you factor out until you get to numbers that can't be factored you're fine. For example if you're factoring out 36 you can start with 18 and 2 or 12 and 3 or 4 and 9 and still end up with the factorization of 2•2•3•3

P(chicago, illinois)