i trust you understand that your daughter simply has to have her bag in the hall at 6AM or whatever, and the Company Manager hands out tickets at the rail station. Doing it on your own, with a room change very two days can get tedious, fast. It's not actually that hard, but it's more intimidating for a first trip to Europe. (I don't mean language, that won't be a problem in hotels and at rail stations.)
You have a vast amount to learn (like which trains require reservations, which trains can't be used with a bargain ticket, where the luggage racks are in each type of coach, what those "Zone A" signs over the platforms mean), and learn in a hurry. I think you should buy Rick's Austria book just for the novice traveler material. I hope you have reasonable domestic travel experience, like what to do when the room is not ready at 10AM, or what a local breakfast might consist of.
I would expect hotels to be busy by the middle of June, so I would not put off decision making. This is an imposing task - Not the travel, but doing it in sync with an already planned tour. If you could change dates to suit train or hotel availability, or substitute cities, it would be a lot easier. I hope you understand that the internet does not provide conclusive answers to "best-lodging" and "must-sees". You are at the mercy of those who happen to see your post, and where they have been. Often, the "favorite" hotel they recommend is already sold out, because they read that it was someone else's favorite! So you have to, say, read Trip Advisor, where you need to screen for phony or useless reviews, and read ten reviews before you put a place on your list of five to try and book in each place. This is hours and hours of work.