Here's a situation where promoting to queen is the only winning move:
1 h8=Q! wins
in 7: 1 ... b1=N+ 2 Kd3 (Kb4 is as good) Kb3 3 Qb8+. Or 2 ... Ka3 3 Qb8 Ka2 4 Qb4 Na3 5 Kd2 Ka1 6 Kc1 and wins next move.
1 h8=R? only draws:
1 ... b1=N+! 2 Kc2 Na3+! 3 Kc3 Nb1+! 4 Kc2 and draw by perpetual.
Here's a situation where promoting to bishop is best:
Promoting to bishop
wins in 6: 1 e8=B Kc8 2 Kb6 Kb8 3 Bd7 Ka8, forcing Black's king into the corner where White's bishop and knight can mate. 4 Nc5 Kb8 5 Na6+ Ka8 6 Bc6#.
Promoting to queen
stalemates immediately.
Promoting to knight
gives insufficient material (two knights versus bare king).
Promoting to rook
wins, but is not best, because the quickest win is in 8, e.g. 1 e8=R Kd7 2 Re5 Kc6 3 Ka6 Kc7 4 Rd5 Kc6 5 Rd4 Kc7 6 Rd6 Kc8 7 Kb6 Kb8 8 Rd8#.
As luck would have it, this morning, YouTube recommended to me a video discussing a win-study by Selezniev which contains this position:
in which, according to the video, promoting to bishop is the only way to win.
Here's a position (must surely be minimal) in which promotion to knight is the unique quickest win:
This quickest win is
1 c8=N K~ 2 a8=Q
There are other winning moves, but the checkmate takes two or more moves longer.