Unfortunately early morning connections are poor, e.g. leaving at 7.59 it's three hours to Riomaggiore with changes at Lucca, Pisa and la Spezia. For a later arrival, it is possible to reach Monterosso with only one change at Viareggio if you leave at 10.02.

To see connections on trenitalia websites, enter Montecatini Terme and the Cinque Terre village of your choice, as each has its own train station and there is a different pattern of services to each.

Thank you both for your responses.

We just did this last week from Pescia, which is only a few stops from Montecatini on the Florence-Viareggio line. Total travel time to CT by train was around 2 hours each way. Driving to la Spezia might have saved us a half hour or so each way, but we preferred to avoid the hassle of driving and finfdin parking, etc. in La Spezia.