From Salerno to Capri, in August the ferry/hydrofoil would no doubt be the best bet. In March we took the bus from Salerno to Amalfi, which took under an hour, but it's a change of bus and another hour to Positano, and on from there. And this was off-season. Do the ferry.
From Salerno to Pompei, the regional Trenitalia train takes less than an hour, although it drops you off at the main Pompei station, not Pompei Scavi, which is the main entrance to the ruins. However, it's only about a 20 minute walk from the main station to the back entrance of the ruins, and if it's not too hot it's definitely a pleasant stroll through Pompei proper. In fact, near the city hall there is a very cool monument to 9-11, with an actual beam from the Twin Towers.
Just a word or two on Salerno. We stayed there 5 nights--we'd take daytrips to Amalfi or Pompei, but would time it to return to Salerno in time for a nap, then a walk along the lungomare by the sea around sunset, then dinner in the Old Town, which doesn't start serving until around 8PM. Just wonderful--you're going to be glad you were 'forced' because of availability to choose Salerno.
RE: Florence, you want as much time there as you can--we did 5 nights. Soak up the vibe, which is unlike anything else I've experienced in Italy. Small town feel, but so historically significant. For example, the Sassetti Chapel on via Tornabuoni is a place you can walk right in during the day for free and see beautiful Renaissance frescoes. There are little gems like this all over Florence. And don't miss the Mercato Centrale for great prosciutto, honey, and a beef sandwich for 3 Euro at Nerbone.