Don't bother stopping.
Pisa is a bit of a detour. While it would make a great stop (you can see the tower on the quick and leave), it is not worth the extra miles.
If you are stopping in Florence, make sure you stop for more than 1 hour. It is a great city that definitely deserves to be visited for a few days. It is not cheap, but one of the best places in the world to pick up fashionable designer gear and see gorgeous art. If you are hitting Florence spend at least a day there and visit the Uffizi galleries and the Dome, then go strolling around the old city.
Pompei is south of Naples, I doubt you'll be stopping there on your way to Rome. It could be done as a day trip from Rome though, its is about 3 hours driving time to Pompeii from Rome.
BTW, why are you so interested in Vicenza? If you have never been to Italy before and are not returning anytime soon, wouldn't it make more sense to visit Venice?
As for a timeframe, the typical Venice-Florence-Rome tourist tour of Italy usually takes about 10 days. 1-2 days in Venice, 3-4 days in Florence and 3-4 days in Rome with daytrips to Cinque Terre from Florence and to Pompeii from Rome.
Hope this helps.