We will be traveling from Siena to Pisa by train for the day, continuing on to Como later that day. Should we reserve our train tickets for both trips in advance?
I see nothing but regional trains on the Siena-Pisa trip, so there's no advantage to buying in advance other than avoiding a delay in a ticket line if you for some reason do not use a vending machine. You will not save money by buying that ticket early, and you cannot reserve seats on a regional train.
Pisa to Como is different. There are all-regional itineraries, and you'll always spend some time on a regional train, but some of the departures involve a leg on a faster train (Freccia, Intercity, Thello) somewhere along the line. For those itineraries, you may save some money by buying early, but the lowest promotional fares for the fast-train segments will be non-refundable/non-changeable.
This will be a long day on the trains. Take a look at the schedules and see what you think. I prefer the Deutsche Bahn website for ease of use, but you'll need to go to Trenitalia for fares.
With a couple of exception all of the trains are Regionale. There is no advantage to purchasing a Regionale ticket on-line because the ticket comes pre-validated with other restrictions. There is no discount for Regionale tickets - same price if you buy early or late. No seat reservations available. No seat !! Stand till one becomes available at the next stop. Buy them at the station.