There is no official LDS doctrine on the subject, and the idea that everyone gets to choose where they want to end up makes no sense anyway. Obviously, some people get born into better circumstances than others, and with people being more likely to want to choose better circumstances than worse ones, clearly there are not enough "good births" to go around, to give everyone what they would ask for.
The idea, insofar as it exists in LDS culture, can probably be traced back to Saturday's Warrior, a musical from the 1970s that became very well-known and popular among Mormons due to its positive message and extremely catchy soundtrack. Unfortunately, the story told in the show depicts several points related to LDS doctrine--in particular, regarding the pre-existence--that could most charitably be described as "questionable," including showing a family together in the pre-existence as the same family they would be on earth, and showing two other characters together as each other's "one and only" who were destined to be married to each other.
These ideas have no solid foundation in LDS theology, and at least once I've heard a General Authority in General Conference specifically deny the idea of a predestined "one and only" which, in his words, had unfortunately found its way into LDS culture through the influence of "a well-intentioned stage play." As the answer to the linked question points out, there are some cases in which certain significant people were foreordained to be born to a certain lineage, but there is no doctrine declaring that such is the case for everyone, or even for a significant fraction of everyone.