First time in italy

No, 7 days is not adequate, even assuming that you're not counting arrival and departure days.

“Would 7 days be adequate?” No

...and do a day trip to Florence

While the high speed train puts Florence ~1 1/2 hours from Rome, I don't consider this a day trip. You listed three places. 7 days would hardly be adequate for any one of the places. At least you didn't throw in CT and Venice like a lot of folks do.

Stan's comments are spot on. You are in the "wish" stage of trip planning and don't yet have an understanding of the basics of travel and sightseeing in Italy. If you don't already have a copy, I suggest you buy the Rick Steves Italy 2018 guidebook, https://store.ricksteves.com/shop/p/italy-guidebook and a copy of Europe Through the Back Door, https://store.ricksteves.com/shop/p/europe-through-the-back-door .

On another post, you say that you have unlimited time but not unlimited funds. These books will enable you to maximize your sightseeing while allowing you to avoid spending huge amounts of money on "ho-hum" sights and activities. Right now, you don't have the overall picture or even a basic idea of how to begin your trip planning in earnest. The books suggested above will help you by putting your travel plans into perspective and giving you insight into the process. Good luck!

You need at least two weeks for what you are proposing.

If your time is limited, cover less ground and enjoy each place more. That is, unless you're the type that likes to "go go go" and see as much as possible.
I prefer slower travel. With 7 days in country (excluding departure and arrival days) I would recommend no more than two cities. If the 7 days include arrival and departure, I recommend staying in Rome. There's more than enough there to keep one busy for a week.
From there, you can also do a pretty easy day trip to Pompeii.

We would have 2 wks at least

No way. You would need 4-5 days for Rome and 3-4 for Florence. Did you forget Venice?

Want to see italy in sept-Oct 2019 Rome,Florence and the Amalfi Coast. Best ways to travel between areas and have read its best to stay in Rome and do a day trip to Florence. Would 7 days be adequate

Then you post

We would have 2 wks at least

So which is it?

vstabl,

It would be really helpful if you could post more detailed information about your proposed trip, such as.....

• total amount of time you have available for the holiday?
• places you most want to see in Italy on this trip, ranked in order of preference?
• airport you'll be flying from?
• have you previously travelled to other parts of Europe?

Where did you read that "its best to stay in Rome and do a day trip to Florence". That's not true and I can't imagine anyone writing that.

With more detailed information, the group here can provide more detailed replies to help you plan your trip.

Look at packaged tours, also Rick's suggestions https://www.ricksteves.com/europe/italy/itinerary

Tours have the efficiency of buses delivering them to the doors of the hotels and museums, so they are optimistic in their timing.

We would have 2 wks at least.

vstabl, please refer to the info requested in Ken's post? And are you traveling from the U.S. or a different country? Besides WWII, what are your other interests? Without more information it's pointless to offer advice as we don't have enough to go on. We don't know if your two weeks are just for Italy or for Florence, Rome, the Amalfi Coast Berlin, Oktoberfest (which is in Munich) + a third country...which isn't sanely possible in 2 weeks and would be a load of transport costs on a limited budget even if it was.

I'll also mention that Oktoberfest in Munich is a very expensive time to go as hotel rates soar during the festival. You would want to make reservations for your accommodations as early as possible

https://happytowander.com/oktoberfest-costs/

We are spontaneous really not tour bus people we like to see things
and if not interested to move on really like out of the way things,
little towns, diamond in the ruff places.

But your list of desired destinations so far are anything but "out of the way" or "little towns". Berlin, Munich (Oktoberfest), Rome, Florence (which I've never seen advised as best day-tripped from Rome) and Amalfi Coast are all either cities or heavily-visited tourist magnets. So some time with some guidebooks would be time well spent to figure out where you really want to go and what you want to see when you get there.

I'd drop the Amalfi coast and save it for another trip.

Rather than shuttle on the train back and forth between Rome and Florence, split the trip into 2 three-day stays, or pick one or the other for the entire week. No, seven days isn't adequate, but it is enough time to get a taste and want to go back.