Don't take high-speed deluxe trains; and avoid trains that are coming or going across borders - they charge more. Take local and region trains and travel 2nd class; it's comfortable, fairly clean and reasonably fast.
Don't buy train tickets on-line; avoid paying an additional service fee. Buy tix at the station - save money and aggravation. At some stations, roving attendants in green jackets are on hand to help you use the automated ticket purchase machines. And remember to stamp the ticket at the little yellow box near the platform before you board the train.
In Florence, we stayed at Casa Santo Nome di Gesu, a B&B in an active convent in Piazza di Carmine. It is a spotless, old palazzo wtih Ikea-furnished rooms and a nice garden, literally seconds from the Brancacci Chapel with its magnificent Massaccio frescoes. Very good buffet breakfast with many choices.Some people may not like is that you have to be in by 11:00 or 11:30 p.m. (I don't remember which) or you'll be locked out, There is no elevator, but the walk up and down the beautiful staircase is a treat. Otherwise, it's a superb location, excellent value and very peaceful. Only one nun spoke English when we there, but others spoke a variety of languages.
In Venice, we stayed at a budget hotel less than five minutes from the station. It's Santa Lucia down Calle de Misericordia, a narrow alley-like passage off the big pedestrian-mall street. It was quiet, clean, very friendly and about 20 or 30 Euros cheaper than any other place we considered. A bargain in Venice!
The big attraction in Venice is...Venice. Sadly, the tourist areas are jammed! And you can't eat or sit down on the street! We loved walking night and day around the city, poking into quiet little communities, sitting in a cafe and watching the people, who were all very friendly. At a couple of craft shops, we were welcomed to come in and just watch the artisans at work without any mention of buying something.
Have fun!