I can't think of a better place to stay in Florence. 5 minutes walking from the tram to the airport, 8 minutes from the central train station. 10 minutes tops to any museums or attraction you are planning to visit. This is the place to stay.
The only thing you should be cautious about is that it is a shared bathroom for 4 bedrooms. It can be hard to shower between 8-10 am... but if you do it before or after, should be fine.