Summer esp July/Aug sucks. As early as possible in June works for Italy/Greece to avoid mobs of crowds and unbearable heat.
In terms of advice for first timers - soak up ambience. In other words you do not need 3 days in Venice. There is no touring you need there - just being. Approach visiting Europe and esp Greece and Italy from a European perspective. Sit and eat, just be. You do not need to go to 101 tourist attractions

Def go to the bigger ones, I'm not saying don't see anything, but don't feel like you must check off the list of 25 places or whatever you must see or you've wasted the trip. There's so many nooks and crannies so to speak. A day trip from Rome to Ponza or Orvieto for example. Passing Pompeii to see Herculaneum. Sitting at St. Marks and listening to the live band and enjoying the ambiance and desserts. That's "seeing" Venice.