If you're riding a motorcycle on UK roads, you are legally required to wear a helmet. In addition, both the helmet and visor/goggles you wear must bear the BSI kitemark or equivalent.
Aside from your legal obligations, a helmet needs to keep your head cool and your brow dry. You need to be able to concentrate, so your helmet should be padded securely and should dampen road noise without making you deaf. It needs to maximise protection without ruining the experience of riding. Many helmets now include extra features like anti-fog pinlock visors, bluetooth, ride-to-rider comms and some even have a rear-view mirror.
SHARP - The Safety Helmet Assessment and Rating Programme - is a programme from the department for transport that independently tests helmets and boils the results down to an easy star rating. They also provide a wealth of important information about how to try on and properly fit a helmet before purchase.
There are six main types of helmet to choose from, depending on your use case.
A full face helmet is the default choice for the majority of road riders. It features a solid chin bar and protection all the way around the head, with a clear polycarbonate visor to see through. The visor flips up to control fogging. Decent sound insulation and ventilation keeps you cool and comfortable at motorway speeds. Premium helmets could include better sound insulation, bluetooth for your tunes and hands-free calling and integrated sun visors.
A flip up helmet is similar to a full-face, except the chin-bar rotates upwards with the visor attached to convert into an open-face. The hinge for the chin bar adds some weight, and reduces the protection compared to a full-face helmet. This type is favoured by tourer or cruiser riders because you can have wind in your face at low speeds, and comfort, quiet and safety at high speeds.
An open-face helmet protects the top, back and sides of your head to a similar degree as a full-face helmet. However, they omit the chin bar entirely, and some may not include a visor. Protection is reduced in a wide variety of situations such as a forward collision, debris being kicked up from traffic in front of you, or even a bird strike. But they do give you the wind-in-your-face feeling without the added weight of the modular helmet.
A half-helmet just protects the top of the head, and maybe some of the rear and sides. They don't provide enough protection to be legal on UK roads, but they are popular in countries where helmets aren't required, such as the US.
Off-road helmets are similar to a full-face helmet. They protect all of your head and have a fixed chin bar, however there are some specific adaptations. They have a long peak, a pronounced chin and no visor for much better ventilation while riding at lower speeds on a hot day. The lack of visor means you'll need to bring your own glasses or goggles, which actually makes cleaning easier. They are unlikely to include luxuries like bluetooth or sun visors.
These are hybrids of full-face and off-road helmets. They have the pronounced chin bar and sun peak, but they're shorter so that they don't catch the wind when riding at high speeds. Better sound insulation and interior padding also keeps you comfortable on a road journey. They usually include a visor for road use, but let it fold up so that you can use goggles on a trail. It won't be as good as either a dedicated full-face or off-road helmet, but you do only need the one.
While it is a legal requirement, wearing a helmet shouldn't be a burden. As you can see, there are lots to choose from and they will enhance your riding experience rather than spoiling the fun. Just like with choosing a motorcycle, you should have a look at what's out there, research some that you're interested in, look up their SHARP rating and then go and try some on.