US:
For a lot of these, the change in words is a slight change in meaning.
I'd like to postpone the meeting for Monday? -not correct
I'd like to postpone the meeting until Monday? - preferred
I'd like to postpone the meeting to Monday? - still ok, but I would prefer "until."
I can't make it to the meeting. - I have something else to do at that time and won't be at the meeting. The other thing cannot be rescheduled.
I can't make it for the meeting. - I have something else to do at that time and won't be at the meeting. The other thing could be rescheduled, but I won't reschedule it for the meeting. I could reschedule it for something more important.
Can we reschedule our lesson? - "reschedule" is to put the lesson at another time.
Can we rearrange our lesson? - "rearrange" means to study conversation and grammar first, and vocabulary second rather than the usual order.
I'd like to schedule a meeting. - pick a time and date for a meeting
I'd like to arrange a meeting. - pick a time, date, people, venue, and topic for a meeting (it is a much broader word than "schedule")
I'd like to set a meeting. - somewhere between "arrange" and "schedule."
I'll have to move our lesson to next week. - moving the meeting that was scheduled this week to next week.
I'll have to move our lesson for next week. - moving the meeting that was scheduled next week to some other time.
And finally- both of the following are fine.
Please pick the day and time slot that suits you best.
Please choose the day and time slot that suits you best.