Have a look at Accommodation in Florence for an overview - there's a link to a website where you can look for accommodation.
Yes, you will need to organise accommodation before you arrive. However, I don't think this means you have to actually sign a lease - you can book yourself into a backpackers at first, for example, and take proof of this with you, as well as a letter detailing your plans for finding accommodation, when you apply for the student visa. You chould give your local embassy a call to double check on this point. Where are you moving from?
There are loads of online apartment websites to start you off. Be prepared to be shocked at the price though - a lot of tourists go this route which drives up the price. Try these guys for example: http://www.oh-florence.com/en/florence-apartments/ or this one http://www.apartmentsinflorence.net/