Ignatius undoubtedly sailed from Asia Minor to Italy, with several stops along the way to pick up other prisoners of Rome. The Times of Ignatius by Patrick Henry Reardon is a nice website describing the possible routes these ships often traveled. Reardon also mentions that most of the time, these boats were no different than a normal merchant vessel.
Sea trade was a large part of life to the Roman people. The Romans first began to trade across the sea when the city of Rome was growing so large that enough grain could not be grown to handle the food demands of the inhabitants. Therefore, the Romans quickly developed large vessels that could sail at speeds of 4 to 5 knots and carry hundreds of tons of grain or other goods. The average speed of these vessels enabled the ships to make the trip from Ostia (the nearby port that served Rome) to Africa in two days. Although normal trade trips could go very quickly, other sources (such as Strabo) inform us that short trips could sometimes take months. Although the Romans typically remained in the Mediterranean Sea (the mare nostrum, or our sea, according to the Romans), a few bold captains occasionally ventured up as far as Britain. However, the Romans themselves were not as adventuresome and typically left these voyages to other captains.
Along with the highly developed sea trade industry, the Romans also had a strong navy. This navy was probably strongest in the 1st Century CE, as it began to decline in the 2nd. The navy was comprised of several types of ships, the most prevalent being the warships. The warships were long, narrow ships controlled completely by oars. These ships had one, two, or three rows of oars, according to contemporary representations. These ships were very tight and normally not very stable or seaworthy. They were usually manned by slaves and the navy did not care if the ship went under. The ships had a long beam extending under water that was used to ram holes in enemy ships. Although the Romans used this bronze covered ram, they also employed land techniques and often boarded enemy ships by way of a gangplank or boarding bridge. This plank had a large iron spike at the end of it that was used to embed the plank into the enemy ship hull. This plank was found to be quite cumbersome, however, and was replaced by a light ladder. The navy also included several Greek designed ships such as the Trireme and also the Roman Quinquereme.
See a picture of a Termini Boat