Renting long term in Florence Italy

How long? Season? Budget? What constitutes "best" in your definition?

Less than or more than 90 days?

If you need a permanent residence, you'll need an Italian immobliare which can be Googled "Immobliare Firenze".

If more of a long-term vacation rental, an oft-overlooked source is Sabbatical Homes

What is best for you?
Cheaper?
More convenient for public transportation?
Safety is not really an issue in Florence since violent crime is extremely rare to non existent and petty crime (like car burglary) can happen anywhere in the city.
Any place within the city works. The cheaper places tend to be the areas where the working class lives, like Novoli, Firenze Nova, Isolotto, Soffiano, Brozzi, Peretola, Le Piagge, which are for the most part the periphery areas on the west of the city center. Those are not my favorite, but they aren't unsafe. Generally the farther you stay from the city center, the less you pay, unless you are on the hills. But you can find properties that are better than average (or worse than average) in any area. If I had plenty of money I'd probably choose to invest in properties on the hills near Piazzale Michelangelo or Fiesole/Settignano or even Careggi. But some of the hills may not be the most convenient if you don't have a car.