any suggestions on things I should buy in advance? thanks!
Anything popular that you want to see. Today they all need reservations.
A lot depends on when you're going. I recommend advance tickets for:
In Rome:
Borghese Gallery (all entrance is by timed, reserved ticket only)
a Vatican complex tour (of the Vatican Museums and St. Peter's Basilica)
the Coloseum
In Florence:
None may be necessary; it depends on when you're going and what you want to do. I pre-booked a Uffizi tour, but otherwise didn't pre-book anything. I believe the Accademia is pretty popular and you might want to get pre-reserved tickets, but I didn't want to go there.
As recommended above, here are the ticketing sites you should use for these most-visited attractions....
...for the Vatican Museums (Rome):
http://www.museivaticani.va/content/museivaticani/en.html
...for Galleria Borghese (Rome):
https://www.tosc.it/tickets.html
If it doesn't come up in English, you can change that under "menu" in the lower right corner of the page
...for the Colosseum (Rome):
https://www.coopculture.it/en/the-colosseum.cfm
This is a somewhat complex website, and tickets (general admission and tours) release on a pre-announced schedule found in the right column of the page. Click the [++] to open the ENTIRE schedule for 2020.
....for the Uffizi and Accademia (Florence):
http://www.b-ticket.com/b-Ticket/uffizi/default_eng.aspx