Should interviews be arranged by less-preferred schools first?
This is a common strategy, but it can backfire on you in the following way.  

If you interview for the position that least interests you and are given a job offer, you may have to respond to that offer before you have a chance to complete the other interviews (or before those institutions are ready to make an offer.)  If this happens you may be faced with the choice of accepting an offer from your least favorite institution or refusing that offer and then running the risk that none of the other interviews will result in an offer.