Hey I did this trip in August. It was such an awesome experience and I definitely recommend it.
Have the hotel book you a private transfer from the airport to the hotel. I found that the best option as you dont have to deal with shady Taxi drivers and them ripping you off. You will know the cost ahead of time. Just bring Euro though because the transfer drivers dont accept card. It is about 55 Euro. I gave 60 Euro (extra 5 for a tip). The cheapest way to do it however is to take the train. If you never have been in a foreign country before this may be difficult to figure out. Private transfer is the best I think.
I found it easiest and cheapest to stay in the hotel your tour ends and begins at in Rome. Dont have Topdeck book it for you as you will end up with a super small room at an outrageous price. Book your stay directly with the hotel as you can get a bigger room for a cheaper price but remember to book early. You can book online. If you need to call the hotel they all speak English pretty well.
You meet in Rome at 3pm for a walking tour where you actually see soooo much of Rome. It goes until pretty late at night. I saw everything I wanted to. I believe you also have a free day in Rome as well to do things like take a tour of the inside of the Colosseum.
Lastly, I would suggest doing all optional activities! Definitely do the Blue Grotto in Capri. If your lucky maybe your tour guide will book a speed boat trip around the island. That was soooo amazing definitely my favorite part but not all the tours do that. If you get to Capri early enough you will have enough time to do that and go visit Positano. It will just be an extremely long and tiring day.
Its a wonderful trip I am sure you will enjoy. Going with Topdeck even makes it better. Let me know if you have any other questions.