Rome Florence Venice Trip - what tickets need to repurchase

What sites are you interested in seeing in each city? Are you in each city for a week, or is one week being split between 3 cities?

You should buy your train tickets from Rome to Florence to Venice assuming you are not trying to drive to each.
Get a Rick Steves guide book and do your own tour, or have the hotel arrange a tour, or buy separately a tour of each city when you get there.
With only a week I assume you should split it between two cities and do a day trip; this way you know or not if you will need to return to Italy again.

I have been to Italy several times and do my own tours using guidebooks and just from liking art and Italian food forever.

The Vatican Museums ticket needs to be purchased in advance. If you find all the basic tickets already sold out on the Vatican website (quite possible), there are earluer threads on this forum suggesting some options.

I believe tickets for the Uffizi and Accademia in Florence also need to be bought ahead of time. I'm not sure about Venice.

Since they admit only a limited number of visitors each day, both the Borghese Gallery and the Domus Aurea in Rome must be booked in advance; I don't know if they are "MUST SEE attractions" to you, but I love them.

There is no reason to wait in line in front of the Uffizi and the Accademia to get a ticket when you can do it online, but purchasing in advance is not mandatory. Same for the Vatican Museums and the Colosseum.

Just as a side note, I don't believe the Colosseum even sells tickets onsite anymore. Both the coopculture and PArCo Archeologico Del Colosseo websites indicate as much:

From the Coopculture site:
"Reservation required online and by phone also for the same day of the visit."

From https://parcocolosseo.it/en/visit/opening-times-and-tickets/faq-tickets/
"Can I buy my ticket at the ticket office?
You can buy the ticket only online through the page Timetables and tickets or through the App ParcoColosseo. The indications to download the App for free can be found on this page."

So yes, you need to make timed-entry reservations for this one.
Also for the Borghese, as Dario mentioned.
https://galleriaborghese.beniculturali.it/en/

Climbing the dome at the duomo in Florence requires a Brunelleschi Pass and timed-entry reservation as well.
https://operaduomofirenze.skiperformance.com/en/store#/en/buy

Uffizi and Accademia:
https://www.b-ticket.com/b-ticket/uffizi/default_eng.aspx.html

Vatican Museums (general entry tickets may already be sold out for later this month)
https://m.museivaticani.va/content/museivaticani-mobile/en.html

Quick question? How many nights are you spending in each city? A week isn't very long, especially if it includes arrival and departure days plus transfer time between them.