I have two. Both 3/4 DOT. Both have good air vents (front & rear). I like the Bell modular helmet (on left), especially with the two visors, one clear, one dark - both anti-fog. My favorite though would be the black Speed and Strength - I refer to it as my hooligan lid. It's much lighter than the Bell.
I wear a 3/4 Bell 500 Custom. Since Triumph has a wide range of offerings (street, cruiser, adventure, classic, etc.) you'd be hard pressed to find a consensus for helmets, but among the classic riders, the overall style is best represented by Davida. Though the brand itself isn't particularly common, the look is often emulated.