Watch your valuables and watch out for scammers, often dressed as Roman soldiers, who encourage you to take a snap with them then harangue you for money.
I agree that the city tour bus will be a good way to get around and see the sights. There is a decent transport system but the plum route -up to the Vatican - is known as the pickpocket express. Gangs work together, bottle in tourists as if it's a crowd and go through pockets.
So as you don't want your break spoiled, stick with the tour bus!
If you are with kids, places like the Vatican Museum and the Capitoline Museum are going to be very off-putting.
You can get a combined ticket for the forum and the colosseum. Again, beware scammers as you approach the colosseum who will tell you that it's about to close so come with them to beat the queue, or that they are official guides.
You can actually make sense of the colosseum for yourself without a guide - or just stand near some of the groups! Much of what I have overheard being told to groups is utter nonsense.
Hope you have a brilliant time!