For me, The Pantheon was the most intriguing. Built in the 2nd century AD, and an unbelievable sight at night. There's some great tourist trap restaurants around the front of it, but worth eating at given their location.
You'll notice 'new Rome' is about 15-20 feet higher than any of the ancient ruins...it's really cool how they've just built above the old city. Drink lots of water, you walk all day.
The Pantheon:
And to some this may sound extremely boring...but honestly buy one of those 'Your Guide to Rome' Books and carry it around. There will be times where you see something and want to see what the hell it is/was...the book comes in handy.