Hi Paula, you will love that tour! Yes, definitely arrive early!
When we took that tour, it began at Lake Como. We flew into Malpensa (Milan), and immediately took the train to Verona for three days. It’s a very nice city to get acclimated to Italy and easy for tourists. You could stay there a couple of days and then take the train over to Venice. Mantova is close to Verona and has some wonderful Gonzaga museums, plus the piazzas are very traditional. Otherwise, the default suggestions for Verona are usually Padova or Vicenza.
Another place if you flew into Venice, instead of heading to Verona, would be to go to Ferrara - an hour by train. There’s a castle in the center of the city. Amazing food, plus it’s a direct train over to Ravenna for the stunning mosaics. But, for a first trip to keep it simple, I’d send you to Verona..
I really like Italy and have been there ten times. Milan isn’t where I would suggest someone stays for their initial time in Italy.