Honest question (not trying to sound sarcastic or anything): Does it matter who starts the game? I've always thought that finishing the game demonstrated a bigger endorsement from a coach.
Starting a player shows respect to your veteran leaders. Ending a game means you're one of the best 5 players on the team.
People can talk about starting line up or closing line up and all that but every team has a line up that is most used and that line up is usually the starting and closing line up. Last season, the most used line up for the Celtics was:
Smart
White
Brown
Tatum
Horford
That line up played 432 minutes and was +103 overall. The second most used line up was the same but Grant in for White, 179 minutes, -5.
The most used line up in the league last season was SAC:
Fox
Hueter
Barnes
Murray
Sabonis
That unit played 900 minutes for a +56. Continuity of the most used line up is generally a pretty good indicator of team success. Teams that are able to keep a core "best" unit on the floor the most, tend to win the most or at least play to their fullest potential. It is not a perfect correlation of course, but a pretty good one.
That point about unit continuity is why I don't think it is a good idea to try and change your units from game to game based on match ups. A team should know what their best unit is and that unit should be on the court the most, and in most cases, start and close the game. Let the other team adjust to you. Injuries and other factors can force a team to use different line ups and when that starts to happen, teams tend to not win as much.
Even at the end of the game, in most cases, you should close with your best unit. There can be situations due to fouls or who is hot or maybe you are behind and are trying to change things up, but in general, the best thing for a team is to close with their best unit, not try to adjust to match up to the other team