amanda,
It would have been prudent to post a bit earlier, as it may have been possible to get some discounted tickets, especially in Italy. Leaving this to the last minute probably means that you'll be paying full price for tickets.
It would help to know whether you've travelled in Europe before, as you'll need to be aware of how to change trains, finding the right platforms, etc. There are some potentially expensive "caveats" to be aware of when using public transit in Italy. If you need more information, post another note.
All of the trips you'll be making are relatively easy by train. You can research each of the solutions using the bahn.de website. I'm not sure a Rail Pass is the most cost effective option in your case, keeping in mind that most of the trains you'll be using are fast trains which have compulsory seat reservations. The reservations are not included with Rail Passes, so you'll have to pay for those separately. Rail Passes are usually not a good option for Italy, as trains are relatively inexpensive, especially when discounted tickets are pre-purchased. One other point is that Pass Holder reservations on French trains are limited, and once the quota for a particular train is sold-out, you wouldn't be able to buy reservations even if there were seats available.
Some information on each of the routes you'll be travelling.....
- Paris to Lucerne - one of the shortest trips is a departure from Gare de Lyon at 10:23, arriving Lucerne at 15:05 (time 4H:42M, 1 change at Basel SBB).
- Lucerne to Venice - one of the shortest trips is a departure at 08:46, arriving Venezia S. Lucia at 15:40 (time 6H:54M, 1 change at Milano Centrale).
- Venice to Florence - using a high speed Freccia or Italo train, this trip will be 2H:05M (no changes) to Firenze S.M. Novella (numerous departures to choose from).
- Florence to Rome - again via high speed Freccia or Italo, this trip will be about 90 minutes (no changes) to Roma Termini.
Note that the reservations on high speed trains are specific to train, date and departure time, so you can only board the one train specified on the ticket. If you're caught without valid reservations on trains in Italy, you'll be subject to hefty fines which will be collected on the spot.
"and I need to finalize asap to have my tickets shipped to US in time. Yikes!"
No need to have tickets shipped. Use www.capitainetrain.com and you can print your tickets at home. The website may not be able to sell tickets for trips originating in Switzerland, but you should be able to get the others there. If you want to purchase tickets for the trip from Lucerne to Milan, use the sbb.ch website.
If you decide that you want a Rail Pass, you can purchase one from THIS WEBSITE and I believe these are shipped from the U.S.
Happy travels!