Aside from parade speeds (like the DGR), I ride with a full-face helmet. An open-face helmet will not protect your mouth, nose, jaw, etc. if you have contact with the ground or other objects. Imagine having your jaw ground down and ripped off by asphalt. Not a pretty image.
Try on as many models as you can to find the right fit. It should be snug and not allow movement independent of your face but not be so tight that it is uncomfortable after 15 minutes. Also note that the liner will give a little as the helmet breaks in and give you some additional room. You do not want slop in the fit.
If you wear glasses, make sure you can slide them on after putting on your helmet. My Bell modular full-face, for instance, is extremely difficult to use with my glasses.
Do NOT buy the cheapest helmet you can afford. By the best helmet you can afford that fits. You only have one skull.