Modular helmets are full-face helmets that have a front section that can be flipped up to reveal the rider's face and temporarily turn the helmet into an open-face helmet. These can be more comfortable than standard full-face helmets, while offering more protection than open-face helmets or half-helmets. The best type of modular helmet depends on what style you like, but regardless of what it looks like, it should be DOT and Snell approved.
The Department of Transportation (DOT) produces standards for helmet safety and approves helmets that meet these standards. The Snell Memorial Foundation also produces standards for helmet safety, and theirs are significantly higher and more rigid than those produced by the DOT. Purchasing a helmet that meets both sets of these standards is well-advised since the helmet is the most important part of a rider's gear, and it is foolhardy to go riding without a quality helmet in place. In some cases, it is even against the law to not wear a helmet or to wear one that is not DOT approved.