Fastest and least transfers from Venice to Monterosso It?
Use either the German Rail (Bahn) webpage or Italian Rail (Trenitalia.com) for schedules.
The Swiss site rail.ch works well too. You can do that trip with a single transfer (in Milan) if you want, but the 2-transfer trips are a bit faster, by about half an hour.
Sherri, The "fastest" train on that particular route is about 5H:28M, however it has two transfers (Firenze & Sarzana). That appears to be your best option in terms of both of the criteria you mentioned. The schedules and fares probably won't change much, so you might consider the train departing Venezia S.L. at 08:27, arriving Monterosso at 13:55 (second class fare €52, reservation required for the first leg). The arrival time is good for Hotel check-in. Happy travels!