Jesica,
I have to agree with Lee in that your travel plans are a bit too ambitious. I don't believe you've allowed adequate travel times between some of the cities you'll be visiting.
As this is your first trip to Europe, my first suggestion would be to try and find a copy of the Guidebook Europe Through The Back Door. If you have sufficient time before your trip, you can order a copy from this website. The book includes information on things like Itinerary planning, packing, currencies and especially "rail skills".
Keep in mind you'll lose the first day in flight times and time zone changes, and you'll be jet-lagged for a day or two after that. It would be a good idea to take things slowly for the first few days.
The route you listed is not the most efficient, and has some "backtracking". Rather than go from Barcelona to Paris and then back to Rome, my preference would be a budget flight from Barcelona to Rome check www.vueling.com) and then start working your way towards Paris.
I'd also suggest dropping a few days in Brussels and perhaps add at least a day or two in London. Also, what is the time frame for "Firenze - Venice"? If you're planning on seeing both cities, your plans will need to be revised. You might consider visiting Lucerne instead of Zurich.
Realistically, I believe you'll have to drop at least one (and maybe more) of the cities on your list. As Rick often says "assume you will return". If you could provide a slightly "leaner" list of cities, it would be easier to suggest a more realistic route.
What time of year were you planning to make this trip?
Good luck with your planning!