Best bet is to look at trip advisor and narrow down some accommodation that is recommended but fits your budget. Then look them up individually and compare reviews and prices.
Your question is a bit too wide, you don't give your budget and it's difficult for people to answer such a broad question.

perhaps the best website for accommodation is www.booking.com
Trusted reviews, instant booking.
For train travel look at http://www.seat61.com/

Consider rail, but also consider bouncing around on cheap flights.

If you go to www.skyscanner.net and pull up flights for the WHOLE month of September from your most far-flung points, like Barcelona (or Prague) to "Everywhere" you'll see cheap flight options to different countries that will save you hours if not days, and big bucks, to cities you might ordinarily not think of connecting to.

All schedules and prices for September might not be loaded yet, so you might want to look at May to get a full sense of who is flying where cheap. (You can fly from London to almost anywhere cheaply). You will generally be limited, however, to 44 lbs. of checked baggage, and some airlines will charge you some bucks for any checked bag, and limit your carry-on.

Since you mentioned your father's ove of Tuscany, and since all of your other destinations are large cities, consider staying a few nights in a small Tuscan town. While Florence is part of Tuscany, it has a very different feel from the smaller towns most people think of when describing this region. Also, given the reason for your trip, which I totally understand, it seems like some time with nature might be what you are looking for. In addition to Tuscany, consider perhaps some time hiking around Munich or Czech Republic or northern Italy.

But I hesitate slightly in making these suggestions, because you already have a long list of destinations, so don't really have time to add more. You listed 9 locations, so in 30 days that's about 3 days in each location, not accounting for travel time in between, so it's usually more like 2. You may want to consider cutting the list down. (As mentioned above, Barcelona would be an obvious choice as it is the most distant). In other words, just think carefully about what would make the best trip for you...constant moving around or more time to really get to know a place? A full diet of large cities or also some time with nature? Only you know what will be right for you.