Regional trains don't sell out (most of your trips are on those trains). They work like the NYC subway. First come first served. If no seats are available, you just stand up.
The only segment, among those in your list, potentially on high speed trains, which may be reserved in advance, is portions of your last segment to Venice (some portions are on regional trains still, since Vernazza is served by regional trains only).
High Speed trains also are never sold out. Occasionally, but rarely, the standard class is full and you either have to wait for the next train (which will almost certainly will have seats available in all classes) or buy a higher class seat, like Premium or Business (about 25-50% more $$).
However reserving high speed trains in advance might offer the chance of buying discounted SuperEConomy or Economy fares. Those fares start selling on line 120 in advance of travel date, and they are gone by the time of your travel. However be aware those fares are restrictive. After a specific train is booked with those fares, you can't make changes later and you can't get refunds if you change your mind. So if you are not sure about your travel dates and times, just buy the tickets at the station when you are ready to go. If you are reasonably certain of your travel time and date from Vernazza to Venezia Santa Lucia, you might see if it's worthwhile for you to buy that segment in advance:
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