Some of you might visit a country or city in Europe and explore it in depth in a few days. Others explore a few countries during one quick visit. While it is easier for some to get a visa on arrival or enter without a visa, for others it is a long process to obtain a Schengen visa that might only be valid for 30 days. Explore Europe at a pace that works for you.
Depending on how much time you have to travel in Europe, plan ahead carefully on what you wish to accomplish from the trip: visit a few cities with a Eurail Pass, rent a car and drive out into the countryside, take a river cruise, etc.
There is no correct or incorrect way to travel and explore Europe because visa, length of stay, budget, interests, etc., are different for everyone. However, if you can, avoid the months of May through August. I highly recommend the off-peak season.
Consider this Pxley story as a plate of tapas or a wine tasting event. The story does not cover the countries and/or cities expansively, but provides you with a taste of possible tidbits.