Yes, wear a helmet. I have MX and street styles--never found a "dualsport" type that fit. If a helmet doesn't fit, it's a waste of money. For any helmet to work well, it must fit well. Lots of info can be googled about how to fit a helmet.
Generally, the better ventilated the helmet, the louder it is inside. Might as well get used to earplugs for summer riding. Generally, dirt riding in any temperature requires a lot of ventilation, so I have only one dirt helmet.
SNELL certification is for young, fit men crashing race cars at 200+mph. Twice. Therefore, SNELL certification means minimal helmet damage at lower speeds, such as TW speeds, and a crushing helmet is an energy absorbing helmet. A tough helmet that does not fail transfers energy to the head inside--not good. DOT certification is required in most states. I have four street helmets. One for summer and one for winter for the TW. Both have fairly soft, crushable shells and styrofoam, with thick, cushy pads that can be changed out to modify fit for maximum comfort and safety. One for summer and one for winter for the CB550, with a more stout shell, thicker styrofoam, and minimal cushy pads for comfort. The CB550 helmets would be expected to provide better impact resistance and more energy absorbtion than the TW helmets, reflecting the ~35-45mph difference in normal operating speeds of the two bikes.
All of my helmets are Bell, because they fit my head with minimal cushy padding needed to provide even pressure all over, so loads will be evenly distributed throughout the bone structure of my head in a crash. Did I mention my top priority for a helmet is good fit so that it works properly. Also, all my helmets are full face, since statistics show nearly 40% of crashes involve the face or part of the helmet covering the face. Face, or part of the helmet that covers the face, that is the question. Seems like a no-brainer to me.
All my street helmets have reasonably priced replacement face shields available. I gave up on tinted face shields after being caught out after dark. Instead, I put masking tape over the top part of the visor to limit solar gain. It works kind of like the visor on a baseball cap and keeps my eyes shaded, especially when the sun is low. I once was pulled over due to the tape, and the cop asked how I saw stop lights. I leaned my head back and looked up--the helmet moves with the head so the tape really isn't an impediment to good vision. I do carry 2 pairs of tinted glasses on each bike, amber and dark gre. They glasses come from the sporting goods department at Walmart. The dark grey glasses are polarized numbers from the fishing department that cost about $5. The amber glasses are from the shooting department and cost about $6. Both are sort of flexible and fit comfortably under helmets. The grey glasses are for sunny days to reduce glare, the amber glasses are for cloudy days to increase contrast. Both are cheap enough to replace every few months as the lenses become scratched bounciong around in the tsnk bag, or when the arms or frames break from conforming to helmet use, two problems I've had even with expensive brand-name glasses.
My dirt helmet takes goggles, Bell brand from Walmart. I bought some replacement lenses and tinted them with cheap window tint film from Walmart--dark grey aand amber.