The most popular types of cooking boards are wood and plastic. Stone is not a practical cutting board because stone will punish, nay, DESTROY, your knives.
Most serious chefs prefer wood boards because they are gentle on your knife edge. The drawback to wood, however, is that it must be cleaned by hand, using warm, soapy water and a brush, sponge or rag. A wood board should NEVER be washed in the dishwasher. Wood boards require additional periodic upkeep because with use, they will become scratched, nicked or etched. They must occasionally be sanded to remove these marks and then treated with a food-grade mineral oil to keep them from drying out.
My preference, however, is flexible plastic cutting boards. Plastic will not do damage to your knives and caring for these boards is considerably easier than caring for wood insofar as these boards are dishwasher safe. I never worry about bacteria on my plastic boards because the dishwasher heats the water to temperatures far beyond anything the human hand could tolerate, and far beyond the temperatures required to kill bacteria.
Another benefit of the flexible plastic boards is that after you've assembled and prepared your ingredients on the board, you can fold up the edges and carry the items to whatever vessel you're using (bowl, pot, etc.), tilt the board and slide the entire pile right into the mix. No messes, no spills.
The drawback to plastic, of course, is durability. A quality wood board will last for years, while the plastic boards are more susceptible to nicks and cuts from your knives, and you certainly can't sand a plastic cutting board. Once it becomes too marred, you must replace it. However, where a quality wooden board can cost close to $100, or sometimes even more, flexible plastic board run about a dollar apiece. I usually keep half a dozen or so on hand, as I often use multiple boards when I'm preparing a dish. My budget can handle replacing half a dozen buck-apiece plastic boards every six to eight months, and the added convenience of their flexibility, coupled with ease of cleaning and the peace of mind I have in knowing that all those microscopic nasty little critters are zapped in my dishwasher make the plastic boards my cutting boards of choice.