Rome wasn't built in a day, and it's very hard to see in a day, because. . .
1) The schlep from the ship is not trivial. You'll spend several hours roundtrip just doing that.
2) It's not a convenient city--things aren't centralized. It's rather a sprawl, and a very crowded, bustling sprawl at that.
Therefore, as first time visitors, your only real option is to take the rather pricey all-inclusive tour. You will see the important things you want to see, while keeping your blood pressure under control in the process.
Here's hoping you'll be impressed enough to come back to Rome for the week or two that it takes to really get "inside" it. It's a wonderous place. Hope you enjoy it.