Hi echo,
Maybe watch this video https://www.youtube.com/watch?v=V2VcEkPaeF4 to gain some insight into Rome's city centre and its outline -- an overview and good pointers about the centre and visiting the main attractions.
Some other helpful videos https://www.youtube.com/user/ItalyGuides
Additionally, check out The Roman Guy Rome videos. https://www.youtube.com/user/TheRomanGuyTours They are a popular tour company, but they have quite a few videos about Rome with helpful suggestions and tips.
They are pretty good for a beginner visitor to Rome. Sean is one of the company's leads and narrates most of the videos. They are fun to watch and laid back.
Naturally, any suggestions or tips you read about or watch regarding attractions, restaurants, etc, it is always best to check actual websites for policies, time changes, pricing, photo taking, etc.
The Vatican, St. Peter's, The Borghese Gallery, and The Colosseum have strict bag policies. With the exception of The Borghese, the others allow small backpacks, cross body bags of "about" 14" - 15."
Anything larger going into The Vatican or St. Peter's would most likely have to be checked - a hassle for you to go and retrieve your belongings after The Vatican visit. But, if you must, there is a free bag check area below the steps of St. Peter's Basilica (off the Piazza.) That would be the easiest to retrieve large bags, etc. Also, there are restrooms down the hall.
The Vatican and St. Peter's have official security/police outside and inside.
The Borghese Gallery did not allow bags in the past - giving out plastic bags for any valuables that did not fit into pockets. Now they are allowing or have been allowing "small" purses - very small.
The Pantheon (Church) has been allowing bags. There are laymen monitors at the door - not official guards - or that I have seen the last several times. They are there for crowd control and to sort of "eyeball."
Keep in mind that time of year (high and low season) will affect a lot of things. It will ultimately be up to guards or whomever for allowable "anything."
Elyssa, who has the Romewise YT is also very good. She lives in Rome and is super nice! https://www.youtube.com/channel/UCYYrGa2k0QCB_AvF01YCpgw
I have been to Italy in September as well as December. September will still be warm and is considered the high season.
Here is another curious site to view https://www.skylinewebcams.com/en/webcam/italia/lazio.html
There are also drop downs for other areas of Italy to view.
You can view the most popular and populated attractions and areas of Rome. The cams give a nice "bird's eye view." You will clearly see there is no need to drive in Rome. It is a very walkable city - an outside museum with beautiful architecture and facades.
Get "lost." That can be fun. With that, you can come across any surprise around any corner - a cute little Church, a small cafe to sit and rest a bit, a small market to purchase a panino and/or water.
On one trip to Rome, in December, I took a side street (around lunchtime) just mainly for curiosity - heading to The Trevi. I began to hear music - horns. I followed the music. I came upon a "marching band" with the musicians dressed as Santa, horns, a drum, playing Christmas songs. People were clapping, singing and dancing along. Good time.
Have fun. I love Rome!