The travertine panels that cover the façade if St. Peter's church in the Vatican, for example, originally covered the brickwork of the Pantheon, Hadrian's massive reconstruction of Agrippa's temple to all the gods. (Agrippa was a long time favorite henchman Augustus and would have succeeded Augustus if Augustus had not outlived him.) The missing stone from the Colosseum is spread all over Rome. Even the Palace of Versailles in France was partially built of spolia (reused stone) from Rome. Popes, Cardinals, and noblemen built their churches and palaces of looted stone, and all routinely "granted" marble blocks to sculptors who gleefully ripped them from the fabric of older Roman buildings. One of the white marble steps of the Temple of Castor and Pollux in the republican forum was reworked in Michelangelo's marble shop into a base for the equestrian statue of Marcus Aurelius in the Campodoglio. The poor picked up the scraps and incorporated them into humbler structures.
The July/August 2000 issue of Scientific American's sister publication, Discovering Archeology, has an article on one type of Roman stone, Purple Porpyry, which quickly became the symbol of the Emperors. Other types of stone, particularly the marbles were also prestigious. Gialo Antico "old yeller", the various Verdi (greens), the Rossi (reds) and rosae (pinks), Neri (blacks) and Bianci (whites) all were valued. The very rich could afford to use Lapis Lazuli for decoration but not for architecture. Clear colors of marble (neither flecked nor streaked) were prized for sculpture.
The only places where one today can get an impression (but only an impression) of the grandeur of ancient Roman stone construction are the massive Christian basilicas of modern Rome, in public monuments in European and American capitals and in some old bank lobbies. Even in the best of those, however, the scale is much smaller. The Lincoln Memorial in Washington, DC, for example, has Lincoln sitting on a Roman curile throne modeled after a similar statue of Constantine that stood in the Maxentius/Constantine Basilica in the Roman forum. The six-meter-tall Lincoln statue fills the center hall of Lincoln's marble-covered memorial. The Constantine statue was almost twice as big and occupied only a curved apse to one side of one of the three huge marble clad halls in his basilica. The Massive church of Santa Maria degli Angeli off Piazza della Republic occupies only a small part of the Baths of Diocletian. St. Peter's, massive though it is, occupies about the same ground space as the remains of Nero's Domus Aurea, but the Domus Aurea ruins are only a small part of Nero's Palace. The other edge was on the Palatine, and the area now occupied by the Colosseum was the fishpond in the middle of Nero's courtyard. The best way to get a real idea of the scale of Ancient Rome's marble clad structures is to stand at the base of the statue of Giuseppe Manzoni at the bottom of the Aventine hill and to look across the long trench where the Circus Maximus stood at what is left of the Imperial palaces. Also, while you're looking, remember that the big statue behind you would have fit neatly under the grandstands of the Circus Maximus which were only half as high as those of the Colosseum.
Although we can only get a small-scale idea of what Rome looked like, we can still easily see examples of what the types of stone looked like. The best way, of course, is to wander Rome with an eye out for architecture and decoration. The Oxford Archeological Guide to Rome has a few introductory pages of text on the different kinds of stone (and other building materials), but what you need is pictures. There are books about Roman stone in better Roman bookstores and they (like the Oxford Guide) can be ordered online. There are several Internet sites, which offer good photos of different stones which you can use if you have a reasonably good color printer. In looking at these pages, note that, out of respect for the Roman and Italian heritage of marbles and related stones, modern stone names are rendered in Italian regardless of their provenance.
Encyclopedia Britannica on marble composition, uses, and quarrying: http://www.britannica.com/eb/article?eu=52003&tocid=0&query=marble&ct=
Families of Marble: http://www.stonecarver.com/marble.html and varieties in alphabetical order: http://www.stonecarver.com/marble-a.html.
Colored marbles, granites, bianco carrara (for statuary): http://www.cmtmarble.com/materials.htm
Web site of one of Rome's biggest travertine stone supplier, Fratelli Poggi: http://www.poggibros.it/english/index.htm