taking the train from Rome to Venice

When you get within 4 months of your travel date, go to www.trenitalia.com and you can buy SuperEconomy tickets for a lot less than the walk-up price. These are nonrefundable, nonchangeable tickets with seat reservations. Since you will probably have fixed hotel bookings, there is no reason not to commit to a specific train booking. There is a train every hour, so just decide when you want to go.
Look at that website now for prices 4 months or less from today to get an idea of prices and how much you will save by buying in advance.
Also, if you travel on a Saturday, they have 2 for one tickets at the base price. Must be bought on-line at least one day ahead.

Not sure if your trip is already set in stone. But for your itinerary it would be best to fly into Venice (VCE) and return home from Rome (FCO).

If your flight in and out of FCO is already set, then it would be best to go to Venice first upon landing (about 4 hours by train). Then, after spending 3 or 4 nights in Venice, return to Rome and spend the last portion of your trip before flying home.

Trains can be purchased ahead of time (up to 120 days prior), a few days before, or even just minutes before you depart at the station.

If you pre-purchase online, you have a chance to get hugely discounted SuperEconomy or Economy fares. The catch is that once you book one of those tickets at those discounted fares, you can't change them or get a refund if you miss the specific train you book (or if you change your mind). Therefore if you buy those fares you must be reasonably certain of your plans.

If you buy a full fare ticket (called "base"), you can buy at any time and you can make changes later. I generally buy them just minutes before I depart or a day or two before at the station. Trains do not run out of seats, however in some popular routes, like Venice to Rome, they might run out of "Standard" class seats (that would be the most economical class) if you buy just minutes before departing with an early morning train (sold out seats in standard can happen only if you leave on trains departing before 10 or 11am, otherwise it doesn't happen). In that case you'd need to buy a higher class, or wait for the next train about 1 hr later.

If you go to Venice upon landing in Rome (as I suggested), do not pre-purchase discounted tickets. The chance of a flight being late and missing the specific train you book is too high.

Prices and schedules are below. October might be too far ahead, but you can get an idea of schedules and prices by using an earlier date, even this week.

www.trenitalia.com
Use the Italian spelling of stations:
ROMA TERMINI
to
VENEZIA SANTA LUCIA.

If departing from the FCO airport station use: FIUMICINO AEROPORTO

There are three levels of ticket pricing - Super Economy, Economy, and Base. Both SE and E are limited in quantity and the numbers available will vary by train and time of day. Early and late trains will have more available and not so many for mid-day. Once those tickets are sold they are gone. SE and E come with restrictions - basically no refund, no change - very limited exchange with E. The Base is full fare ticket with no restrictions. All trains in Italy except for Regionale require a reservation prior to boarding. Since you know your schedule it would make economic sense to try to find SE tickets on-line prior to leaving home roughly at the three, four month mark. However, SE are dirt cheap and go quickly.