Is it better to teach young players to record their move first and then make it? Or should they be taught to move first and write later? Is one considered better etiquette over the other?
It hasn't always been so, but these days (at least according to FIDE rules) it's illegal to write your move down before making it, outside of some situations in which a draw is being claimed or the game is being adjourned. Here are the exact details as to when a move should be recorded (with the most relevant part italicized):
8.1. In the course of play each player is required to record his own moves and those of his opponent in the correct manner, move after move, as clearly and legibily as possible, in the algebraic notation (See Appendix C), on the scoresheet prescribed for the competition.
It is forbidden to write the moves in advance, unless the player is claiming a draw according to Article 9.2, or 9.3 or adjourning a game according to the Guidelines of Adjourned Games point 1.a.
A player may reply to his opponent’s move before recording it, if he so wishes. He must record his previous move before making another.
I believe the reason that it's against the rules now is because writing the move in advance could be construed as some sort of analysis aid. (I'm not arguing that that's a good reason for the rule; it's just what I understand to be a rationale for the rule.)
The common advice for kids was to record the move first, then check it one last time and look for missed opponent moves, before playing it. This is a way to slow down to avoid rushed moves and reduce blunders.
Despite the rules, Elizabeth Spiegel in her 2019 chess educator of the year talk continues to recommend to her kids the pre-writing of moves for blunder checking. She said that in almost all circumstances for kids no one will have a problem, and if anyone makes an issue of it it will be adults.