Jordan,
First of all, congratulations!
Now, regarding your travel plans. Your proposed Itinerary is probably feasible, but it seems a bit "busy", especially considering the occasion. I've found some of Rick's proposed Itineraries to be somewhat ambitious for the average traveler, and seem to be a better fit for experienced travelers.
As I read your Post, this is your plan (correct as required):
Day 1: Depart home (SEA?)
Day 2: Arrive Paris / CDG
Days 3-5: Barge trip
Day 6: Depart via train for Venice (trip will be ~10H:58M with minimum of 1 change; a FULL travel day).
Day 7: Venice
Day 8: Depart via train for Florence (trip will be ~2H:40M)
Days 9-10: Florence
Day 11: Depart via train for the Cinque Terre (which village?) Trip will be ~2H:22M to La Spezia & then a short time to one of the villages.
Days 12-13: Cinque Terre
Day 14: Cinque Terre to Siena (trip will be ~3H:19M, possibly 2 changes)
Days 15-18: Siena & Tuscany (note that EACH driver will require an International Driver's Permit to drive in Italy, which must be used with your home D.L.; fines can be applied on the spot for failing to produce one - GPS would be a good idea - usual minimum age for car rental is 25)
Day 19: Train to Rome (trip will be ~3H:41M, possibly one change in Florence - will depend on which train you choose).
Days 20-23: Rome! (if you take a day trip to Pompeii, it will be a LONG day - as someone else suggested, Capri would be better left for another trip).
Day 24: Fly home from Rome / FCO
Regarding the rail pass, you might do some "number crunching" as it may not be the most cost effective. The only long (expensive) trip is Paris to Venice. Note that reservations which are compulsory on some trains are NOT included with a Pass so you'd have to pay that separately.
As usual, I'd suggest reading Europe Through The Back Door if this is your first trip.
Good luck and happy travels!