RyanAir can be a pain in some ways because they tend to use secondary airports located a bit away from the city to help keep costs down, but it is definately not a reason for a write-off. They are definately the cheapest and most convenient way to travel around Europe. I don't care id the airport is 20 km from the city centre if it saves me 100 EUROs and gets me there 5 hrs sooner.
I did the exact trip to Italy that you are planning. I did it in 9 days. I only regret not visiting the Italian Lakes.
If you fly into Venice first, your first impression of Italy will be quiet and slow paced. As you move on to Florence and Rome, scooters, pedestrians and noise will increase significantly. If you perfer quiet small towns you may want to stay just outside Florence and go in for the day. Pisa is only an hour train ride from Florence, although it doesn't have too much character. There are also sorts of amazing small Tuscan towns just outside of Florence.
Rome can take months to see it all but you should give yourself a minimum of two full days: one for the Vatican and another for the Forum, Coleseum and other sites.
If I were to go again for 9 nights I would do 2 in Venice, 2 or 3 in the Italian Lakes, 2 in Pisa (or a Tuscan village) and 3 in Rome.