If you can navigate this web site, I doubt you will have much trouble booking your own travel arrangements. I would become familiar with only mapping tools such as Google or Bing maps. Both tools will not only allow you to search for hotels, restaurants, museums, etc. but they'll also provide directions including public transportation options.
Some things to remember:
September is on the downhill side of the peak travel season. Still a lot of tourists but things are loosening up quite a bit. Trains only need to be pre-booked if you want to get the cheapest fares but if convenience and flexibility are more important, I would just wait until you arrive to purchase them. And, if you are traveling in areas where the high-speed trains don't go (Cinque Terre), there really isn't any reason to pre-purchase (if that option is even available).
I would pass on the Geneva leg if only to maximize your time in Italy. You can easily fly into Venice and out Florence (or Pisa or Rome). You can use Venice as a jumping-off point for other local cities (Padua, Vicenza, Verona - all on the main train line) and/or take an escorted day trip into the Dolomites.
Florence is a really good central location for exploring Tuscany but Lucca is much more quaint and less overrun by tourists. There are also many (many!) escorted day trips into the Tuscan countryside from Florence or you can take the train/bus to several hill towns in the area.
If you have your heart set on the Cinque Terre, you might consider a flight into Milan, Turin, or even Genoa.
If you are entertaining the thought of driving in Italy, be sure to get an International Driver's Permit from your local AAA office before leaving. It's mandatory and many car rental agencies won't even rent to you without you showing it to them. Being stopped by the police without it in your possession is a hefty fine...
Ensure you know the PINs assigned to all your credit cards. If you intend to purchase train/bus tickets at kiosks, you'll need a Chip & Signature or Chip & PIN credit card (non-chipped debit cards will not work). These machines REQUIRE the PIN or the sale fails. If you haven't received a PIN from the issuing bank, contact them at least 6 weeks before traveling.
If your card becomes compromised while traveling, you can call the issuer to have the lock temporarily lifted in order to pay for hotels, cars. etc.). It's a royal pain but it can get you out of a jam. (Gee, do you suppose it's happened to me?) I would also make sure you have enough funds to cover almost any expense in a checking account accessible via a debit card. I always take a spare linked to a back-up account as well...
Also, NEVER - EVER log into a financial account via public WIFI. This goes for ANY WIFI abroad. If you feel you will need to log into bank portals over WIFI, get a private VPN service BEFORE you leave. I use one that costs $40 a year and covers up to five devices under one subscription. (Google VPNs and read up on them. They're pretty easy to understand but the short story is that they encrypt your communications so people can't see what you are doing.)
I would also consider getting a pay-as-you-go SIM card for you smart phone upon arrival in Italy. It will make things so much easier and pleasant.
