Paris to Versailles is easy: You take an RER train (I think it's line C, it's the yellow one) straight there. I think r/t it'll only cost you about 7 euros.
Paris to Nice, well, probably your flight will end up being either the same price or perhaps even cheaper than if you took the train. If you really want to take the train, it's best to buy tickets there. Go to the Gare du Lyon and ask the ticket agent how much it will be, I'm guessing at least 50 euros, maybe as much as 75. The TGV goes like a bat out of freaking hell down to Marseilles-- almost 200mph or so with no stops. That's about 2-3 hours or so, then you'll hop on another train in Marseilles (or you may stay on the same one) to Nice, which is about 2.5 hours because they can't go quite as fast. It's a LOVELY ride if you end up deciding to do that!
Sorry, I don't have any information about Italy to give you, but for train schedules and fares you can look at
http://www.bahn.de and click on "international guests" for the english version.