ok, I've done the really short trip, the medium trip and the two week trip.
The short trip I went to Rome for a couple of days and then Florence for one day. They are close enough to do that.
Medium trip was Rome, Sorrento, Naples, Capri. Pompeii and then ALLLL the way up to Venice for a day.
Long trip (last year) we stayed in a farmhouse near Chiusi and took day trips to Pisa, Florence, Cortona, Assisi and a couple of other small trips. We spent the last two days in Rome - which is not nearly enough time - but since I had already been there I didn't feel like I missed anything - although I think the others did.
I think that a tour would be a good idea. You don't have to worry about trains or driving (I didn't think the driving there was so bad, personally, but it's different and they like to drive in the middle of two lanes for some reason), the hotels are taken care of, etc. But you also miss out on some of the really wonderful experiences of making your way in another country - stumbling around in broken Italian and trying to figure things out.
Amalfi is pretty far from everything so I'm not sure that's such a great place to make your home base unless you plan on kicking back and getting to know your area a bit. If you're trying to see everything, you need to have a plan - and Venice is really far from everything else. Tour is definitely the way to go - or else make your plan to stay in each place a couple of days. Remember that the trains are really good and reliable and usually drop you off in the middle of the city, and don't forget to visit the Prada and Gucci outlets in Perugia.
