Actually, for the end of March/beginning of April, I would skip the Cinque Terre (too much chance of cold, iffy weather) and go to the Sorrento/Amalfi coast instead.
I agree with the above that you should arrive as directly as you can into Florence. If you don't already have your air tickets nailed, look into open-jaw tickets from home: into FLR & out from FCO. Even if it costs a little bit more, it will more than be worth it to avoid booking separate train tickets for Easter Saturday. The Florence airport is very close to the city center and a very easy one to arrive to.
If you arrive in Rome, even bought in advance (the fast trains will sell out for that day), plan on spending extra for the most flexible fare conditions (since you cannot chance the cheapest, no change-no-refund fares, when arriving from overseas to connect to a train journey). Even if you can make changes or get a refund on the spot, expect trains to be pretty full that day, including the slower Regionale that don't require advance booking. Give yourself a large cushion of time between when you should arrive at FCO, and when your train would leave from Termini... several hours in which you can leave your luggage at Termini, walk a bit and grab a meal or fret minimally if you are delayed in reaching the train station (over a late plane, fewer guys working on the Easter week-end shifts at the airports, etc..)
Since you will be there over Easter week-end (with the holiday Monday), plan on at least your first 4 nights - as the holiday will slow you down for sure. I like the idea of doing a tour on the holiday Monday, as the one suggested for Pisa. I share the opinion of skipping Civita altogether this trip. (Save it for a May-Sept trip to the CT, Tuscany & Umbria)
Seriously consider visiting Siena as a daytrip from Florence - if so, add one more night to Florence. IMO, there really is no need to lug all your stuff to sleep there...
Basing yourself in Sorrento, you could use 4 nights (3 full days) for visiting Naples, Pompeii, the Amalfi Coast and Capri (forget Paestum). Naples you could visit on the train day arriving from Florence (on a morning train): you would leave your luggage at the 'left luggage' facility of the Naples train station. You really don't have to fear taking the Circumvesuviana commuter train from Naples to Sorrento at the end of the day (just watch your belongings very closely). I have done it more than once and others here have too.
Save 4 nights for Rome at the end, which would give you 3 full days to visit the city's highlights before you fly home.
So, a nice Easter trip could look like this: 5 nights Florence + 4 nights Sorrento + 4 nights Rome => 3 places to stay => 3 bases for exploring outward => 2 minimally "lost" train travel days (that you can book online in advance, shortly after Christmas).
Remember, you don't necessarily have to be a RS guidebook lemming... it's a great planning tool, not a 'Blue Bible'... ;-)