UPOD;
The great thing about being 20 is that there is less jet lag and less need to stop in a little cafe and look at the world go by. This is going to be a GREAT first time European trip. Forget all those museums and churches. Get a feel for the place and I can bet you will come back again and again.
One suggestion:
Flights in Europe can be late by a few hours at a time and getting from the airport to the center of town may be easy or hard, in other words a little unpredictable and bumpy.
If you can avoid it, I would do less flying and more train. It is flexible and reversible and allows you to change your plans at the last moment.
Oh, one other thing Dublin and Amsterdam totally rule. Spend a little more time there and less in Rome.
the best.