A very important point, indeed! Even before the first word is translated, the translating team must decide which of the families of manuscripts (handwritten copies) they will use over the others, due to slight variations. It's an art and a science, but not an exact science by any stretch.
I think if most Bible-believing Christians knew the amount of arbitrary decision making that went into their translation they would be gravely disturbed - which is probably why many churches avoid the subject!
Thanks for a solid and understandable story!