There are plenty of options to get to Niagara Falls from the Greater Toronto Area (GTA). There is also one major change since the answers to the previous questions were posted: there is now one daily roundtrip GO train between Union Station and Niagara Falls.
If you're arriving in Toronto around 3pm on a weekday, you have plenty of time to take the UP Express train to Union Station, followed by the Niagara-bound GO train, which leaves Union Station at 5:15pm, and arrives in Niagara Falls at 7:47pm (see Table 12 here). While this isn't necessarily the fastest route, it's definitely the most comfortable and consistent at that time of day.
There are more GO trains to/from Niagara Falls on weekends on Victoria Day weekend, during the summer, and on Thanksgiving weekend (in 2019: May 18-20, June 22–September 2 and October 12-14). The only other rail option is the VIA train, which leaves Toronto at 8:20am, and Niagara Falls at 5:45pm (see schedules here). There is no VIA train that calls at Burlington like in your question.
As I'm sure you've discovered, there are other transport modes too (bus, rental car, etc.). In summary:
By Rail (use UP Express to access Union Station: 25min, $12.35 cash, $9.25 Presto)
- GO train service on weekdays: Niagara Falls at 05:19 -> Union Station 07:50; Union Station 17:15 -> Niagara Falls 19:47 (2h32, $21.15 cash, $17.79 Presto)
- VIA Rail service daily: Union Station 08:20 -> Niagara Falls 10:16; Niagara Falls 17:45 -> Union Station 19:41 (2h, prices variable, approximately $20-30)
- GO train service on weekends during the summer (June 22-September 2, 2019) and some public holidays (Victoria Day, Thanksgiving): four daily trains (2h, $21.15 cash, $17.79 Presto)
- Megabus from the Toronto Coach Terminal (use UP Express and TTC Subway, add $3.25 cash or $1.60 Presto and 20 min travel time): departures every 1-3 hours throughout the day (1h45-2h10+ depending on traffic, $12-24)
- GO bus from Pearson Airport (route 40) connecting to GO bus (route 12) in Burlington or Hamilton, using Hamilton Street Railway (HSR, local buses) as a connector if necessary: see triplinx.ca for availability and routing (3h30+ depending on traffic, $21.15-$24.45 cash, $14.89 to $18.39 Presto depending on transfers)
Driving (call 511 or visit 511on.ca for real-time traffic conditions)
- Using only public highways (427 -> QEW, or 427 -> 403 -> QEW), expect a travel time of 1h30-3h00, depending on traffic. Traffic volumes are highest between 06:00-10:00, and 15:00-19:00 on weekdays, and before noon on spring/summer weekends.
- Using the toll highway 407 (427 -> 403 -> 407 -> QEW), expect a travel time of 1h15-2h00, depending on traffic, and a toll of $13-17 (plus any fees added by the car rental company).
Though I don't make the trip often, I've traveled between Toronto and Niagara Falls around 20 times by various modes. I never regretted taking public transit (despite the extra time commitment), but nearly every time I drove, I regretted it eventually.