Wow, you have alot on your plate!
If I had a choice and it was the 1st time to visit these places, I'd focus on those destinations that are in line such as Britain, France and Italy (which I know the best). Or choose Britain, France and Germany.
On one trip, I did a loop of England and Scotland in about a week. London, York (use this as a hub), daytripped to Edinburgh, travel south to Bath, onward to Oxford before returning to London.
For France, going from Paris to the Loire Valley on the TGV to Tours is easy. From there, I recommend going to Provence. I stayed in Avignon and used it as a hub for exploring this region. There are charming towns in Provence. This is where the French Impressionists lived and painted. You can still see the cafe which Van Gogh painted in Arles. From there, it is easy to travel east along the Riviera to Nice (which is also a wonderful hub). I suggest a daytrip to Monaco from Nice. It's very close. Then when it's time to leave, take the train from Nice to Milan.
For Italy, my favorite places are Florence and Rome. If you want to be near the water, the Cinque Terre or Sorrento (a seaside resort town).
Florence, Rome and Sorrento are great hub towns to explore the regions. 5 days in each city at least.
They are chockful of treasures. You will cry when you have to leave if you only set aside a few days for them.
The two cities (Florence and Rome) are tremendous for their art, history, food and people. I cannot say enough about them.
Even if you want to get away from the chaos of the city center, from Florence you can take a bus to Fiesole up in the hills above the city. You can escape to the seaside from Florence and venture to the Cinque Terre. I've stayed in Monterosso al Mare, the biggest town.
From Rome, go on the Archeobus tour which will take you outside the walls along the Appian Way. You will see the beautiful villas and you can take a tour of Christian catacombs. It's like the country outside the walls, very peaceful.
If you do go the Germany route, I think Munich has wonderful museums, churches, outdoor food spaces, gardens, etc. Take a daytrip to Neuschwanstein Castle in Schwangau from Munich.
Lastly, consider if you want to alternate visiting cities, small towns, seaside/lake resorts so that you have some variety.
Let me stop here.