rome to naples should i book the fast speed train ahead???

Buy the ticket once you are at the airport station and pay full price. Full price with fastest trains is 64€, but if you are willing to go on slower Intercity trains, you can save that way too.
Savings aren’t that big to justify losing everything in case the plane is late.
No matter what you can be in Naples before 12 noon. To Sorrento you need another 70 min.

You are taking a risk if you book a train departing not too long after you flight arrives. If you book the Super Economy ticket, you save the most money, but if you miss the train because your plane was late, you lose it and have to buy another ticket at the last minute price.

So you can either buy a ticket when you arrive at the last-minute prices - or you can build in a delay of a few hours to make sure you arrive in time (probably) not to miss your train.

Or you can book a cheap ticket now and just take a chance. Tickets to Naples aren't that expensive, so you don't have a lot to lose if you miss the train. Although trains can sell out, there are a lot of daily trains to Naples. Chances are you would get on one without too much trouble.

Everyone has a different preference, but regarding jet lag, I prefer to stay up all day after an overseas flight and just adjust to the local time and not go to sleep until local time that night. It makes for a long, groggy day, but the sooner I get over jet lag, the better I'll feel later in the trip.

My suggestion would be the same as Roberto mentioned. Yes, take the fast train from Roma Termini to Napoli Centrale. After a long international flight, you're likely going to be jet lagged and not in the mood for a long trip.

You will actually be using two trains, the Leonardo Express from the airport to Roma Termini and then a Frecciarossa from Roma Termini to Napoli Centrale. Note that there are two regional trains serving the airport (Leonardo Express and FL-1) so be sure to board the correct train! DON'T forget to validate your ticket prior to boarding or you'll be subject to hefty fines which will be collected on the spot. You'll have reserved seats on the Freccia train so you don't have to validate tickets for that; be sure to note your Carrozza (Coach no.) and your Posti (seat no's).

When you arrive in Naples, you have a couple of choices to get to Sorrento.....

• you can take the Circumvesuviana or Campania Express (trains). Go downstairs to the Garibaldi station to access those.
• you can arrange a private driver and make the trip in an air conditioned car. After a long flight, that will be the easiest choice but of course also the most expensive. Have a look at Monetti Taxi for one firm that you could use. There may be others listed in the RS Italy guidebook.

To address a couple of your concerns, you don't have to buy train tickets in advance. They will be available upon arrival. The person who told you that probably meant you must buy in advance to get discounted fares, because discounted tickets aren't sold on the day of travel. I once took the slower Intercity train from Rome to Naples and I don't recall the scenery being much different from what I see when I take the Freccia trains. It just goes by a little faster on the Freccia.

I've twice gone straight to Sorrento from FCO using Leonardo Express, Frecciarossa to Naples and Cirumvesuviana to Sorrento. As I recall, I was in Sorrento around midday and my flight arrived later than yours. Note that Frecciabianca trains trains take 35-40 minutes longer to get to Naples than other Freccia trains (taking almost as much time as the Intercity), so avoid the few of those that run each day.