Don’t miss lesser known churches - San Pietro and San Giovanni in Laterno are spectacular, to be sure, but there are so many secret treasures. I’ve been to Rome 3 times, for a total of 27 days, never with a tour, and my favorite parts were just wandering, popping into every church we passed.
San Clemente is gorgeous, with a great archeological dig underneath…Santa Cecelia is quietly moving (I don’t know if they’re open all year, but if you can get to the catacombs, and see her memorial there, do so). Santa Maria Sopra Minerva is right near the Pantheon and has fantastic gothic architecture and art.
Santa Maria in Trastevere has breathtaking mosaics. Santa Susanna, the American Church in Rome (where you can find English masses) was kind of non-descript in general, but cannot be missed - it is the home of the Ecstasy of St. Theresa by Bernini -
en.wikipedia.org/wiki/Ecstasy_of_St_Theresa My personal favorite, I think, is Sant Andrea del Fratte, near the Spanish Steps, that contains some of the original angels from the Bridge of Angels.
Speaking of Bernini, if you enjoy art and sculpture at all, don’t miss the Villa Borghese. His sculptures defy description - they are so full of detail and raw emotion, and humanity, sometimes there is the eerie sense that they are real people, trapped in stone. All are remarkable, but my favorite is The Rape of Proserpina, depicting Pluto kidnapping her to the underworld. Last time I studied it for almost an hour. See the Pieta and other works first though - by the time I got to Michaelangelo, I’d been thoroughly spoiled by Bernini, and found it very…blah.
I have lots and lots of recs /tips for the secular historical/pagan side of things as well, but I don’t know if you’re interested

One general one is that if you’re planning on seeing the colosseum, your ticket is good for both the colosseum and the palatine hill across the street - buy your ticket at the palatine office and avoid all the massive lines, you can skip ahead when you get to the colosseum (they’re good from the time bought until I think 1 pm the next day, excluding holidays, ask when you purchase to make sure, if you’re planning on splitting it).
If you want to be in the center of things, and be able to walk almost everywhere (the only time we used public transport was to get to the catacombs, though Borghese is also a hike, but doable if you’re active and have time) look for a place near the Pantheon. We stay at the Hotel Adriano, which is very nice, clean, pretty quiet, great staff, good breakfast, and very affordable - don’t know if that’s because we’re originating in Europe as well though. There’s also an awesome hidden little take out pizza place (authentic and cheap) practically next door, and “the best gelato in rome” aka “most famous”, Giolitti’s, is right around the corner - pay first, then go to the counter with your ticket.
A lot of books/hotels call things “centered” that really aren’t - Pantheon puts you about a 20 minute walk from the Vatican and colosseum (opposite directions, with lots between), 10 from Trevi, 5 from the Spanish Steps.
Have a great time, it’s my favorite city in the world!