I AM TRAVELLING IN 2 WEEKS TO EUROPE WITH 2 TEENAGER, need help how to get speedy, non-stop (if poss

I AM TRAVELLING IN 2 WEEKS TO EUROPE WITH 2 TEENAGER, need help how to get speedy, non-stop (if possible) train from Rome to Florence... where is the train station at in Rome and how much will it cost??? We are staying in the outshirt of Rome in a hotel, zip code is RM 00136. Where should I go for the train station to Florence? travelling in July 15.
I will be flying toronto hotels to Vienna from Rome, then train or private car to Prague... need suggestion which is better to do for time saving, toronto hotels more economical for all of us, I checked the suggested web site of BD BAHN, but a little confused, since I can't find non-stop fast train. If train which station should we go? we are staying in Vienna around the Stadtpark area. what station should we get on? I saw some forumist say Wien Meiding toronto hotels is better, but I cannot find that in my train map... should I go to the airport or the Vienna internaional center area, Kaisemu"hlen station??? Please PROVIDE STATION NAME if you have a more convenient and better location!
A shame you need to fly between Rome and Vienna, you could have taken a direct Rome/Florence to Vienna sleeper train, also booked at www.trenitalia.com and saved a hotel bill, and had a unique European toronto hotels experience, the great international night sleeper express, much more relaxed than flying!
Vienna to Prague starts at 19 euros, book at the Austrian railways site www.oebb.at . Several modern air-con EuroCity trains every day. Go from Meidling, it's in the centre, no need to trek out to remote airports.
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