What are the best options?
Idea of "best" is different for everybody
But since you prefer not to worry about buying tickets during the trip, then the most reasonable option is to visit TrenItalia website (trenitalia.com), select the connection you like and purchase in advance discounted ticket for it (in order to do so, you need to select "MINI" offer among the fares offered, that is the discounted one, which allows you to save up to 60%. Number of discounted tickets is limited, so it makes sense to look for those as early as possible.
We have read about advance purchase but not sure how far in advance we can buy the tickets
As of today (Dec.5) the last day for which you can purchase discounted ticket for domestic high-speed EuroStar trains is January 22, 2012, thus it makes 48 days in advance, while in case of slightly slower InterCity trains number of days even greater - last day here is April 4. We just recommend time to time in March check the website (when all the option will be already on sale) and then make you mind about specific connections.
What stations do the trains depart from?
In Venice it will be "Venezia Santa Lucia" (or Venezia St.L), in Florence - "Firenze S.M.N", in Naples - "Napoli Centrale" and in Rome - "Roma Termini". All the above stations considered to be main and central of the respective cities.