Peter,
Given the time of year you'll be travelling, one other factor to consider is getting a seat on the train. Mid-July is PEAK travel season, so the trains will probably be very busy!
If you're travelling on the EuroStar Italia you'll have reserved seats (these are compulsory) while on the slower regional trains this isn't usually the case.
It's certainly possible you'll have no trouble getting a seat on the Regional train. That route is fairly busy, so my preference would be a reserved seat. If you don't make it on one train, there'll be another along in an hour or so.
As you've never been on a European train, you might find it useful to read the "Rail Skills" section in Europe Through The Back Door or download the free PDF Rail Guide from this website. It helps to have some idea on the way the trains work, and you'll need to learn a few important words (ie: Binario = Track No.).
Happy travels!