When I have been involved at a club usually what happened is:
The previous coaches say which division they think their players should be in. Then Someone with a good understanding of the existing players and with the help of previous coaches data, will then split the players into two groups (e.g. div 1-3 and div 4-6). Usually the training's are over 2-3 courts (if 2 courts about 12-15 players per court).
Once that is done over 2 weeks, the second stage of trials happens where players are put into smaller groups (Div 1-2, div 3-4, 5-6).
At the same time as the first stage of trials new players have about 2 trials. They can then be put into the smaller groups. Obviously if their is an exceptional player or a player coming from another club they usually bypass the new player trials and go straight into one of the groups in the first stage.
Basically it is a divide and conquer strategy. In theory it would work well but unfortunately there is players away for trials. Another issue is the trial process is too short due to the season starting so close to the winter season grand final.
In general existing players are chosen in front of new players if they are similar in skills to reward loyalty. 1st year players are chosen in front of 2nd year players if they are similar in skills and also depending on physical ability. It all depends on age group. I try to get 2-3 1st year players to go with 5-6 2nd year players. Other clubs do it differently. For the summer season one particular club (as long as they will be somewhat competitive) will have say an all 1st year team in div 2 and div 4. Then in winter season they will make adjustments.
At the end of the day I think it is best to create a balance for all teams. For example there is no point a div 3 team taking all the height and then leaving div 4+ to struggle due to having no height. Also when picking a team, balance the team. Too often coaches go for the best talent or focus on the best scorers and then end up with balancing issues. Teams need role players, energy players, defensive players, rebounders, guards that can set up the tempo etc.
A final note is talk to your club on the best procedure on letting players know they are being moved down a division or being moved to domestic. One coach I was doing trials with wanted just to announce the names of the boys that didn't make it in front of everyone. I think that is a brutal approach and depending on the boy could really impact them psychologically for a long time. In the first stage I think a simple email saying which team they are being moved to indicating it isn't final, is fine. In the second stage either pull the boy a side after training (depending on age group might be a good idea to have their parent there as well) and give them feedback on the things they did well and then on the things they need to improve on to be in that particular division or do it by email. Either way feedback is very important. Confirm with your club how they want you to do it