It looks like there are two train stations in Lucca. Which one do I want to arrive at when traveling from Florence (SMN)? Which one puts us closer to town?
You need Lucca. Taking the other one - Bagni di Lucca - will find you in a spa somewhere in the hills far north from where you want to be.
Lucca.
Bagni di Lucca is miles away from Lucca, and is a separate town.
However, it's worth a daytrip to there if you have lots of time!
From the station in Lucca: you walk out front, cross the street, and walk through one of the gates through the big walls right into Lucca itself.
Enjoy Lucca, it's beautiful!