Loads of great tips on trip advisor, including to buy combined tickets for palatine hill/forum/colosseum at the (relatively quiet) palatine hill entrance. Then you can skip the queues at the colosseum. The three of these will take up most of a day.
If they're going St. Peter's, get there for when it opens and they'll barely have to queue.
If they want to do the Vatican then don't even bother trying to go without booking in advance (can do it on their phones the night before they decide to go). Vatican and St. Peter's can be done in the same day.
Most places offer audio tours (or indeed tour guides) but if they want to save a bit of money there's a free app by Rick Steve with loads of audio tours on it. He's a bit annoying but bearable and they really added to the experience.
I loved the pantheon, and sitting in the square with a drink is a must.
They should go into every church they can. Most of them don't look anything from the outside but inside they're AMAZING. I'm not religious in the slightest, but the artwork is honestly mind blowing. The Sistine chapel was a bit of a disappointment after all the incredible churches we'd seen!
I almost forgot the baths of Caracalla! Much quieter than some of the better known attractions and just absolutely awesome.
There's a reasonable spread of attractions but they can be grouped to do a few nearby ones on one day. We stayed near piazza navona and everything was walkable, including Vatican City. Make sure they take comfortable shoes though because my god I've never walked so much in my life. There were times I thought I wasn't going to be able to go on...
Most importantly, they must eat all the pizza and pasta.