This is not science and it's not an art. Do what's convenient for all.
Joan says: This is not science and it's not an art. Do what's convenient for all.
Nancy says: don't try to manipulate your clients or the outcome of the process in any way.
Mack says: This is overthinking it.
Use other logical factors that dictate how you show them, which may or may not include your clients input/preference, but don't try to play psychologist and "outsmart" the process.
Then order is irrelevant. I have shown every which way and it makes NO difference. If they are ready to buy then they will. It is that simple.
btw, as a buyer agent NEVER EVER presume you know what is most or least desirable for them. That is sure to lead to issues. keep your emotions out of it. They are living there, not you. Your job is to find homes close to what they want, not what you think they want and to be the local expertabout teh market etc. I see you did say the homes that "They Think are best" but many agents pick what they think are best.
I schedule the tour of showings by neighborhood (regardless of which home may be their favorite) so as to not be back-tracking all over town. This not only helps the buyers see the neighborhood amenities and make-up better since we aren't hopping from one area to another but also saves on gas.
Prudential Connecticut Realty