Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Minot to Venice as you normally would.
Minot (MOT) is the airport you will fly out of if you book a flight from Minot to Venice. You should not have trouble finding flights to Venice from Minot; the airport handles an average of 0 outbound flights to Venice per day. You should also have plenty of airline options to choose from since 0 airlines have flights from the Minot airport to Venice. It is only a 2.0 mi journey to Minot (MOT) from Minot’s city center.