First Time Europe Travel Help London, Paris, Pisa, Rome, Venice

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We would like to travel from London, Paris, Pisa, Rome and Venice.  We are open to stops in other cities on the way.  Our return flight is from London.  We have 14 days from Aug 01-Aug 15.  Any advice on travel routes and cost saving ideas are much appreciated.  Thank you in advance.

In terms of rail travel and your preferred destinations you pretty much have two major choices:
1) purchase in advance discounted tickets. In most cases those are nonrefundable and nonexchangeable, thus you will be 'tied' to predefined trains and date, but on the contrary you can get a pretty good deal. For instance, Rome-Venice for 46 EUR or London-Paris return from app. 110 USD etc.
2) get a railway pass. It will cost you a fortune, especially since you will need Eurail pass, but will you give you certain amount of flexibility and you won't need to worry about buying cheap ticket long in advance. If you buy a pas, then the only thing you will need to do is just to buy seat/sleeper reservations.
So we just advice you to visit official railway companies websites (eurostar.com , [url=www.tgv-europe.com/en/, www.trenitalia.com) check availability of good offers for your dates. And at the end you will be more "equipped" to make a decision.
Or you can also gives your dates, so we can check the best deals for you and arrive at app. cost of travel expenses for the whole itinerary.

Also might be a good idea to fly one way, either from London to Italy (then go back to UK via Paris by rail) or vice versa - London-Paris-Italy-->fly back to London. There are multiple airline companies serving UK-Italy routes, including low cost airlines, thus you can get extremely cheap offer (usually much cheaper than the train tickets in Western Europe)

Thank you for your prompt response.  Here is what I have so far. 
Depart Miami 7/31 Arrive London morning of 8/01
Paris: 8/03-8/05
Rome: 8/05-8/08
Naples/Pompeii: 08/08-08/10
Florence/Pisa/Venice: 08/10-08-13
traveling back to paris and london for flight 8/15 on

I do want to state that this is a tentative itinerary.  I do not want to see all of Europe in such a short timeframe.  I will be traveling with my 15 year-old daughter.  This is our first trip to Europe and we are very excited.  I do want to point out, that within each stop there is only one sight or attraction that we decided on.  For example, in London we want to visit the Stonehenge.  I scheduled 2 days there, so we could fall where the wind blows us.  In Paris, she wants to eat pastries from a "real" French Bakery and I want to see the Eiffel Tower. Naples, we want to visit Pompeii.  I read that Naples is where we should stay and take a train/bus to Pompeii.  We could make day trip there and explore Naples then move on to the next city.  We are very flexible.  If you see better alternatives or methods to enhance our schedule by cost, time/length of travel, or any other factor, please let me know.  Which train ticket should I purchase?  Both my daughter and I have a ISIC card, if it is of any help.  Again, thank you in advance. 

Ok, so we will just give you the fares for your connections as of now. As result you can take a look, sum it up and make a decision.
London-Paris: for August 3 there are actually tickets available for as low as 65 USD (which is great price for this connection). Those are for 4 pm train. For the morning trains fares are from 121 USD to 148 USD (or 73-89 GBP). Tickets can be bought on EuroStar website
Paris-Rome: on the 5th of August fares for direct overnight train is rather big (from 120 EUR), while for daytime options with change total fare would be even bigger, thus you might consider here flights, which are cheaper (from 60 EUR) and will get you to Rome faster.
Rome-Naples: here you have plenty of options. You might go with purchase of discounted ticket for high-speed ES trains (36-41 EUR depending departure and 1:10) or InterCity (from 18 EUR and app. 2 hours). You can check this fares on your own from TrenItalia website (will need offer called "Mini"). Or don't bother with purchasing anything in advance, but just use regional train, fare is always the same (only 10.5 EUR and 2.5 hours), so you can buy your ticket even 5 minutes before departure.
For Napoli-Pompei - http://www.vesuviana.it/web/en/Orari
Naples-Florence: for morning August 10 there are still discounted ticket for 50 EUR available for high-speed trains (app. 3 hours travel time). For InterCity trains (app. 5 hours) - from 40 EUR.
Florence-Pisa-Florence: everything easy here, because of multiple regional trains for only 5.8 EUR one way. So just come to the station before departure and get your ticket with no problem.
Florence-Venice:  also discounted tickets for InterCity or ES trains available. For instance, for August 12 afternoon from 26 EUR on ES. While regular full fare for ES is 43 EUR, for InterCity - 24 EUR.
Venice-London: here it would definitely make sense to fly, because of expensive rail travel. For instance, for 14th evening there are RyanAir flight for 68 EUR to London Stansted etc.