Train travel

Where are you looking? Since these are all trips in Italy, you should be looking on the Italian Railways website: http://www.trenitalia.com/tcom-en

Yes, fares are different for different trips; like airlines, you pay more if you travel further.
Train prices only ever go up. They start cheap, and as the cheap tickets sell out only the more expensive ones are left. What you might be seeing is higher prices on some days of the week and at some times, because the cheaper tickets have sold out for those trains and only the more expensive ones are left, but other trains still have cheap tickets.

You need to know the correct name of the stations you want to travel between, not the English translated names:
Venezia S. Lucia, Firenze S. M. Novella, Siena, Napoli Centrale, Roma Termini.
And Cinque Terre is as the name suggests, an area with 5 towns in it. Each town has a station, so you need to look for trains to or from whichever of the 5 towns you want to visit.

"best time of day to book" - now, prices never go down, only up.
"best rail line to use" - the quickest. Rail websites like Trenitalia will always find the quickest route from A to B
"book in advance" - Yes, as above, it is cheaper for long distance trains. For local trains (called "Regionale"), the price is fixed, never goes up or down and you pay the same if you buy at the station.
"train travel with luggage, etc." - You alone are responsible for carrying your luggage from the street, through the station onto the train and storing it near your seat. There is no checked luggage, it is all hand luggage.
See this webpage for more info and photos: https://www.seat61.com/luggage-on-european-trains.htm

For Venice to Florence and Naples to Rome, check Italotreno as well. It's a private rail line which services select cities in Italy and has competitive rates against Trenitalia's.

https://www.italotreno.it/en

The Freccia trains are high speed trains, often running on special tracks that allow them to go at 200 mph. Tickets are sold like airline tickets. You get an assigned seat (which often you can pick) several levels of service, like Standard, Business, and Executive with increasingly bigger seats. These are also sold, as Chris describes in discount levels.

He also described Regionale trains. so to get from A to B, may be all Freccia trains, all Regionali, or a combination of both. Per your itinerary:
1. Venice to Florence is a direct Freccia train.
2. Florence to Cinque Terre is likely to be all Regionali.
3. Cinque Terre to Siena is likely all Regionali.
4. Siena to Naples is likely a Regionale connecting to a Freccia.
5. Naples to Rome will be a direct Freccia.

Trenitalia will show all the connections, prices at various times during the day. Prices will very depending on the route and the discount level of the various Freccia connections. morning Freccia trains often have higher prices because that is the business man's (woman's) preferred travel time, and someone else is paying for the ticket. Convenience trumps price. You, as a leisure traveler, have to option of leaving a little later at a cheaper price.

Great information...thanks to all!

Does anyone have experience with the loco2.com ticket service?

Super economy seats? Any major drawbacks for a 2 hour train ride?

Yes, I use https://loco2.com/ regularly. They offer tickets at the same price as the train companies, so if they are easier for you to use than the train company website (either because it is more user-friendly, or because it likes your credit card), do so.
They are a UK-based site, and offer prices in both £, € and US$ (GBP, EUR and USD). Whatever currency you choose, the transaction will be booked in the UK, and you may get hit with a foreign use surcharge on your card.

Like the other recommended European website ( https://www.trainline.eu/ ), they only cover some countries. They both cover Italy, so you could use either, or stick with Trenitalia.

thanks. Just booked with Loco2. Went well. What do we use in place of a paper ticket?

When you bought your ticket, you should have been sent an e-mail with a PDF file attached (I hope you selected "print-at-home"). You need to print out this PDF file and bring it with you.
See this Loco2 webpage: https://help.loco2.com/article/284-ticket-delivery-options
There is a sample Trenitalia ticket here: https://blog.trainline.eu/wp-content/uploads/2015/03/trenitalia_ticket.png

You show it to the ticket inspector on the train when he comes round to check tickets. At some larger stations there are ticket barriers, if you hold up the barcode on your ticket up to the reader it will let you in.

On our train trip from Florence to La Spezia, and then to Vernazza, the 2 stops/train changes are 8 minutes in Pisa,
and 14 minutes in La Spezia.

Another option is 16 in Pisa, and 6 minutes in La Spezia for train changes.

Will this give us ample time to change trains?

Book Regional train tickets in advance?

Traveling from Florence to Vernazza Cinque Terre. Loco2 shows me a regional train, with another regional train connection, and then the cinque terre express. I understand that the regional train fares are fixed and do not require a reservation.

What advantage, if any, would it be to book now as opposed to the day of travel in Oct?
-Can the tickets be sold out, if we waited?
-Is there a chance the price may go up if we purchase them in October?

Thanks!

Regional trains never sell out - if all the seats are taken you can stand. If all the seats are taken and a lot of people are standing it can get a bit crowded.

All reservation trains, which are those trains faster than Regionals, have no standing - everybody is in a reserved seat.

Super economy seats? Any major drawbacks for a 2 hour train ride?

The seats are 1st or 2nd class. Super Economy / Economy / Base are just price levels, all the same seats. Like an airline, you could be sitting next to someone who paid twice as much as you, or half as much, for the same seat.

Regional train tickets . . . What advantage, if any, would it be to book now as opposed to the day of travel in Oct?
-Can the tickets be sold out, if we waited?
-Is there a chance the price may go up if we purchase them in October?

No advantage, except saving time at the station. Possible disadvantage, if you buy in adance you can't decide to travel on a different day.
The tickets cannot sell out. Because they are not for a specific train. They are valid on any train. That is why you have to validate them, to stop you using the ticket twice.
Price - no, it is fixed until the end of 2018.

Thanks for the helpful information.
Just to clarify, if regional train tickets are pruchased in advance, they can only used for that designated date and time? So, if travel plans are changed or if we were late in arriving, we would not be able to use these tickets on another date or time? Thanks.

Regional tickets bought on-line generally can used during a 4-hour window from the time of the first train. So if you miss a train or decide to travel a little later, they are still valid on that particular route. You can also make one date change up to the day before the trip.
https://www.trenitalia.com/tcom-en/Purchase/Regional-online-ticket-and-passes

I would not purchase Regionale train tickets on-line. No advantage, discout, or reason to do so. Regionale tickets have to be used within a four hour window. If you buy on line then you specify a day and a start time - say 0800. Then that ticket will only be valid on that day and during that time window. If you buy it in the station, at a machine, or local travel agency the ticket is not valid until you validate it (time stamp) in one of the little blue/green/yellow boxes near the tracks/platforms. Watch the local do it. Then that ticket is good for four hours regardless of when it was purchased.

Thanks, again!

Going to book our trip from Vernazza to Naples, with a final destination to Praiano by car transfer.

What is the correct train station in Naples in order to be in the correct location for an auto transfer to Praiano?