Skip the line tickets

Nobody skips the security line.

Purchase your tickets from the official sites- not resellers.

Accademia has timed entry purchased in advance
Duomo climb does as well- the Duomo is free- no ticket needed.

St Peters is free- no ticket required- nobody skips security line

Vatican and Sistine I would book an early entry visit to avoid the crowds- from Vatican site or from a tour company
There are many many threads on here addressing how to visit Vatican/Sistine

If you need links to official sites- just ask.

We did a Walks of Italy Pristine Sistine a few weeks ago that was "skip the line." It really does skip the line everyone else takes, but there is still a little bit of lining up. For us, we met at our rendezvous point, then walked over to the entrance while we heard a brief history of how the Vatican City was carved out. We got in line at the entrance to make sure we were first when the doors opened, and during this brief wait (10-15 min?), we had a presentation on the Sistine Chapel (since there's no talking/tourguide presentation inside). All the guided groups did the same thing, some with handouts, some with binders of large photos. Once inside there was a quick security checkpoint & potty break, then we picked up new headsets & did a tour of the museum. We dropped headseats before entering the Sistine, and after exiting, got new headseats. We were able to take the shortcut to St. Peter's only b/c of the skip-the-line early Sistine tour. We were extremely happy when we saw the insane lines we would have stood in had we not gone first thing. There were many, many other tour companies operating, yet we still managed to find plenty of space in the museum. It was money well spent. Walks of Italy and The Tour Guy have RickSteves promo codes.

To clarify a PP's statement: the Duomo (cathedral) in Florence is free to enter, but the line can be long and it's very spartan inside.
Climbing the cupola of the Duomo has a timed entrance, must be reserved in advance, and costs. Upon entering, you'll see the best part of the inside of the cathedral anyway while you wait to scan your ticket and go up the stairs. We chose the Brunelleschi Pass with timed cupola/dome climb. We heard the afternoon was the best time to go, and they were right...especially if you go on a weekend! We used our Brunelleschi Pass to get into the other museums and sites. Keep your barcode handy as you need it to both get through security and again to scan to get through turnstyles/into museums. I had an issue with the scanner not reading the barcode on my phone, and I was really nervous I was going to get tossed out of line. In retrospect, I would bring a paper ticket next time. Everyone else's paper tickets scanned perfectly, but my screen ticket was fussy, especially b/c you have to figure out how much to zoom in on the barcode in the email and where to put it near the top of your phone so it fits under the reader.

We booked a The Tour Guy walking tour of Florence with Skip-the-Line Uffizi and David (Academia). It was incredible and the single best part of our entire trip to Italy. Matthieu and Eriza were so incredibly knowledgeable. They made us fall in love with the art of their city and truly understand the progression from Gothic to Romanesque to Renaissance. I know they freelance for other companies (Walks of Italy), so you probably can't go wrong with either. For those tours, I don't think we waited at all except a hot second to go through security and get new headsets.

In case you hadn't thought of the Bargello, it is absolutely worth it. I know you can purchase tickets online for timed entrances. There are also combo tickets, but pay attention to the days you'll be in town as some sister sites are only open one day a week, and others have early closing hours.

Sorry enbateu but you didn't skip any line at the Vatican Museums. You simply arrived when the security line was short. Then, like anyone else with an entrance ticket purchased in advance, you had no reason to wait in the line to buy the entrance tickets on the day.

It sounds a little like a scam to me, but I am sure the tour was worth it.