If you want to see Tuscany and the Amalfi Coast, don't spend the whole two weeks from Rome. You will be doing entirely too much driving, not have enough time to experience much of the other destinations and Rome is more expensive to stay in than the other areas (even though I do realize you'll be using points).
You are required to purchase all the insurances for car rentals in Italy (credit cards don't cover it) and so a car rental can be a pit pricey, but try
www.autoeurope.com for decent rates. The only place you'll really want a car is in Tuscany. From Rome to Tuscany is an easy drive and there are many, many lovely towns throughout Tuscany you'll want to visit. I've done one-way car rentals before where I picked up the car on the outskirts of Rome (you don't want to drive in Rome), drove around Tuscany and Perugia and then dropped the car in Sorrento and had a driver take me down the Amalfi Coast. (You also don't want to drive any further south than Sorrento.) You can also do the train service to get down the coast. Cabs are extremely expensive in the Amalfi area, so you might want to arrange for a driver ahead of time.
You could also do something like take the train from Rome to Florence and then rent a car out of Florence for the rest of your time in Tuscany. Return the car in Florence and take the train back down to Rome and on to Naples or Salerno (just use caution and watch your belongings at all times in the train stations). You do want to be certian you've purchased seat reservations on any train travel though or you could find yourself packed in and standing the whole way.
There is a Hilton in Sorrento, where you could use points, though it's far nicer to stay further down. Ravello and Positano are gorgeous. There is a good, cheap bus service connecting Positano, Praiano, Amalfi and Ravello.
You'll definitely want to visit Pompeii in your travels to or from the coast.
As for when to book, if you're using miles and points start calling ASAP and don't be discouraged if you don't get what you want immediately - just keep checking back.