I have heard that the best plan would be to travel from Venice to Verona where there will be more options in catching the train to Innsbruck. Is this correct?
Yes, trains from Verona (Verona Porta Nuova station) to Innsbruck/Munich go every two hours during daytime (from 9am to 5pm), so in general it is easier to catch local Italian train from Venice to Verona and change there. However there is also a direct EuroCity train from Venice to Innsbruck/Munich departing everyday at 13:34
I have heard the Verona to Innsbruck section of the journey is through the mountains and is very beautiful, so we would like to travel this section in daylight. Is this possible?
Journey over the Alps indeed rather scenic, so it' definitely a good choice to spend half a day traveling
Could we travel from Venice to Verona and on to Innsbruck in one day?
No problem, travel time between Venice St.Lucia and Verona Porta Nuova varies from 1:10 to 2:15 depending on train type, while Verona to Innsbruck is roughly 3:30. As result passenger can easily manage the whole trip Venice-Innsbruck in a half a day
Is it worth spending a night in Innsbruck or should we travel through to Munich?
Well, Innsbruck is a nice place, but it's definitely smaller than Munich, so in case of shortage of time half a day spent in Innsbruck might be enough (meaning you start from Venice early morning, arrive to Innsbruck around noon and depart to Munich late evening). But if time isn't an issue and accommodation in Munich and Innsbruck are more or less the same price, then why not to enjoy Innsbruck a bit more?
And now a few words about tickets and fares... Here you have a number of options: a) buy in advance discounted ticket for the direct EC train on TrenItalia website (fare is called EUROPA, tickets start from 29 euro); b) don't buy anything in advance, but in order not to pay too much just use a bit slower regional trains from Venice to Verona and then to the Italy-Austria border - Brenner (one though ticket will cost you less than 25 euro and you can purchase it any time, even 5 min before departure). Brenner-Innsbruck ticket is just 7,8 euro and you can buy it separately at any international ticket counter (for instance during change in Verona); c) also possible just to purchase in advance discounted international ticket (same fare EUROPA) from Verona to Innsbruck, this way you won't bother with any tricky "ticket breaks" via Brenner
For Innsbruck-Munich route you can as well buy in advance discounted international tickets (via Austrian Railways website, guide how to do it -
http://europetrainsguide.com/Advice/How-to-Buy-Train-Tickets/Austria-OeBB.html), those start from 19 euro. Also if the number of people traveling is 2 and more, then it might make sense to think about group pass
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