The reason to choose one train over another is speed, frequency, and fewr changes on routes between major cities. For instance, (again I'll use Vernazza) to Venice is 4 to 5 separate trains, and 6 to 7 1/2 hours. Using a mix of Regionale, IC, and Freccia trains, it is 3 or 4 separate trains, and 5 to 6 1/2 hours. The Regionale prices are fixed at 31.50 to 32.50 EUR depending on the route, as low as 32.70 EUR when bought up to 4 months in advance, but as high as 87 EUR when bought day of travel.
Venice to Varenna-Esino is 3 Regionale trains, take a bit more than 6 hours and costs 24 EUR all the time. Using the Freccia it is 4 hours with one connecting Regionale from Milan to Varenna-Esino. It can be as low as 16.60 EUR 4 months in advance or as high as 45 EUR bought day of travel.
Going to Muerren is not as advantageous as Swiss trains are the same price all the time, you can take two Regionale's to Domodossolo for 15.20 EUR in 3 1/2 to 5 hours, then you will be on Swiss trains the rest of the way. It is 73.60 CHF the rest of the way to Muerren all the time.
Muerren to Innsbruck can be done inexpensively because SBB will sell you a saver fare ticket on the Austrian Railjet from Zurich to Innsbruck if you buy it well in advance.