Terry- both the Colosseum and Vatican sights are time consuming. 1/2 days each minimum. You can choose one or the other. Chances are you will love Italy and Rome and will return. Consider this a sampler visit.
What time of year is this and what are you most interested in?
Exactly what time will you arrive? Might try to do a top sight this pm- 4-7?
What time is your departure flight?
How will your energy level and budget be at this point of trip?
Colosseum closing varies- "1 hour before sunset" if you can be here by 4- as long as you just want to visit and don't need an in depth tour- done by 7.
Vatican has pm hours on Fri. We did the early am entry and so very glad. I have to admit I didn't really enjoy the museum, it was just so crowded. But being in the Sistine Chapel with a small group was awesome. I'd say a Vatican visit will consume more time and be a bit more of a hassle because of location.
If your budget is limited and you love art- just pop into every church you can along the way. They are free.
Pantheon is free.
You also can't go wrong with a visit to the Borghese Gallery
If it were me I'd choose just one of those 2 top sights, maybe add a lesser sight.
Colosseum/Forum arrival pm- dinner in Trastevere or Piazza Navonna
Visit Campo de'Fiori market in am, then Pantheon, Trevi/Spanish Steps-/P Popolo (heart of Rome walk).
End at Borghese if time allows. (timed entry- 2 hr limit)
That's easily done in the 1.5 days you have.
We like to walk, so have actually never used any public transpo in Rome- we have taken a cab now and then.
Cabs are usually very reasonable 6-10€?
Cab to/from airport is a fixed rate 48€
Do you have RS Rome guidebook?
See here for "Rome in a day"
https://www.ricksteves.com/europe/italy/rome-itinerary