While it is true that you can’t see „all of Rome“ in 3 days, you couldn’t do that in 2 weeks either, so don’t worry about that. You gotta start somewhere. What’s important is that you pick something that is interesting to you and your travel companion(s). Use an overview site like the Attractions section on Tripadvisor or Culture Trip to find a few things that appeal to you: https://theculturetrip.com/europe/italy/rome/
No need to fill your time up to the brim, if you enjoy a more leisurely pace anyway. It’s not the worst idea in Rome to just allott time to stroll through the city – and visit churches that you pass by and find interesting. There are masterpieces of art in the churches of Rome that would be the crown jewels of museums. And you can see them for free and in their natural surroundings. Also, Rome is full of hidden gems that aren’t necessarily what most people imagine Rome is. For example, the Quartiere Coppedè.
One last note: As I have been to the Vatican Museums in August and in January, I can highly recommend to take the chance to see this famous museum without being engulfed in a constant stream of visitors.