Which trains to take from Florence to Pisa & Lucca

Kathy, I don't want to sound facetious, but if you want to get from A to B, the trains you want are the ones that go from A to B.

Look up trains on the Italian railways site: http://www.trenitalia.com/tcom-en
Just enter from "Firenze S. M. Novella" to "Pisa ( Tutte Le Stazioni )", and a date and time, click on "Search", and it will list all the trains and prices.
Same for Pisa to Lucca, and Lucca to Monterosso.

There are regular (and very cheap) Regionale trains, leaving from Florence's main station Santa Maria Novella (also abbreviated as S.M. Novella or S.M.N.). No need for reservation. Just buy your tickets from the window or at one of the ticket machines. Schedules on www.trenitalia.com/tcom-en (give »Firenze« as your departure station).

My suggestion is to drive from Pienza to Lucca. Park the car and visit Lucca.
After Lucca you can drive to Pisa and visit the famous Piazza dei Miracoli (Tower, cathedral, baptistery) for an hour.
Lastly you can drive your car to La Spezia and return the car there.

That would be my plan. The only issue is time. There is a lot of activities packed in a day and the rental offices in La Spezia close by 7:30pm. Then from there you need to take the train to Monterosso, which is about 20 min by train.

An alternative would be to return the car at the Pisa Airport, since rental offices stay open until late at night. However you still must consider the time you need to take the train from Pisa to La Spezia, and then from La Spezia to Monterosso.

Either way, do what you can, however returning the car in Florence, then heading to Lucca/Pisa by train would be the last thing I would do, because returning the car in Florence, then taking the train from there, is going to eat up at least half of your day.