Our family of 4 (all adults) will be making a 3 week trip to Europe this summer to visit exchange students we have hosted. We will definitely be visiting Denmark (Copenhagen), Germany (Hamburg), Finland (Helsinki), and Italy (Venice). Other stops we would be interested in making include Berlin, Prague, and the island of Sardinia in Italy (primarily to visit other exchange students we have met). On previous trips to Europe we have spent the entire vacation in one country or in one city, so we have no experience traveling between countries.
I'm looking for advice on several fronts. First, should we add on any of the additional stops, or just focus on our 4 primary stops?
Second, is flying between our stops the best option? It is more important for us to spend time with our students than to save a few bucks and lose time sitting on a train. Where is the best place to purchase tickets for travel within Europe?
Finally, is the best way to layout our stops just looking at the map and travel north to south (or vice versa)?