Thanks for writing back :-)
Our reference trenitalia.it is simply the official Italian Railways website, as you see (and no, we have no power to improve that website... although we're certainly going to forward your remarks to them. Please note, however, that the timetable gap you came across is likely to depend on the annual train timetable change, which in 2010 will happen on June 14. After June 14 some trains WILL actually CHANGE THEIR TIMETABLE.)
As for fares, the 'Base', 'Full', 'Flessibile', 'meno 15' and 'meno 30' options refer to special discount fares, where 'meno 15' and 'meno 30 are intended for people younger than 15 and 30 years respectively. We personally always use the 'Base' option.
There are no declared 'stop-over' opportunities at Trenitalia, but you can freely get off a train on your way and take another one later along the same route you were following before (and, obviously, you purchased a ticket for). So, in practice, there IS a 'stop-over' opportunity.
However, please take note that
1) if you buy a ticket, say, from Milan to Lucca, you purchase the opportunity to travel by train from Milan to Lucca ALONG A SPECIFIC ROUTE, which may happen NOT to include either La Spezia or Monterosso (or Vernazza, Corniglia, Manarola, Riomaggiore, i.e. the five train stations in the Cinque Terre area); (in fact, nearly every train route between Milan and Lucca includes Florence, reaching Lucca from North: the main exception is the 9769 FRECCIABIANCA train, which includes Genoa and La Spezia, reaching Lucca from West, but doesn't stop in any of the five Cinque Terre railway stations, although they are located between Genoa and La Spezia;)
2) you always have to validate your ticket before entering your train car (you do so by inserting your ticket in a small box, which marks the validation time). Each validated ticket entitles you to travel on that specific route FOR THAT DAY ONLY...
In other words, you'd better buy a specific ticket for each of your trains.
Nonetheless, you can buy all the tickets you need in advance, and then validate each of those tickets step by step just before you ride a specific train. Doing so, you avoid risks of travelling with a ticket that may be no longer valid.
Our personal advice is that you go in person to the La Spezia railway station, explain your case at the ticket counter and buy all the tickets you're going to need. You don't have to decide in advance WHEN you're going to use those tickets. You only have to tell WHICH TRAINS you're going to ride.
Last but not least, a final note. We recently read that the Italian Railways seem to accept web purchases through Italian credit cards ONLY! This may be another reason for purchasing your train tickets in person, once you've reached La Spezia.
We know: this is a complicated country... ;-)