Ponte Vecchio to SMN is about a 25 minute walk if you are walking normaly, 20-ish if running.
I did that walk twice a day for a few years and i wouldn't recomend it for someone on vacation. Better to be closer to the train station. Also emergencies happen...
There is no need to book regional trains in advance. Once you are in Florence you can also buy generic tickets with only the kilometers written on.