The trouble with trying to do the Amalfi region in 2 or 3 days (Capri, Positano, Pompeii, etc) is that you have to factor in the time it takes to get from one place to the other. It will be go, go, go all the time. You really won't be able to enjoy it all. Pompeii easily takes half a day to really do it justice. You have to factor in travel time by bus as the roads are very twisty and narrow, and traffic jams can occur. Also, depending on the ferry, it can take a while to get to and from Capri. I would try to concentrate on a smaller chunk of the Amalfi coast and not be so ambitious. Make a list of your "must sees" and then if you have time take in some of the other sites. Making a "day trip" from Florence to Pompeii might not be as easy as you think. It is quite a long ride and will take several hours to get there by train, and then once you get there you have to find your way to Pompeii and do the same in reverse to get back. You also have to factor in time for eating, etc... Try not to bite off more than you can chew, because things don't move as fast as they do here in the U.S. If you want to stay in the Amalfi region and are up for a challenge but want a nice place to stay on a beer budget, then I have a recommendation for you. Last year I stayed in Amalfi at a little B & B called "Le Palme Amalfi". Their rooms start at 40 Euro. Here is the catch: Their place is located on the side of a steep hillside amongst the lemon groves. It is 300 steps down from the Hotel Excelsior above and another 656 steps down to the road below leading to town. They have a porter service for your bags. If you would like, I can send to you pictures of its location so that you can see for yourself. The owner's have a restaurant in town and can have dinner brought to you. They have the best lasagna and eggplant parmigiana I have ever tasted.
If you choose Florence, I stay at the B & B "Il Salotto di Firenze" which has very nice and reasonably priced rooms.