I've been gathering some ideas for a fantasy novel and while researching medieval armor, I've noticed that there seem to be a lot of helmets. For example:
I'm sure that many of these different designs were used at different points in the Medieval Ages, but looking back, is there a definite "best" helmet? What were the advantages/disadvantages of the different kinds of helmets?
Just a brief note: with the exception of the so-called "Great Helm", all of the helmets you listed date from the end of the Medieval period, when plate armor became relatively common. I invite you to consider that these helms, while taken to be the quintessential "Medieval" helmets in popular culture, in reality only represented a very narrow slice of the types of helms that were used in Europe during the Medieval period.
With that said, I would probably add on a few other helms to your list that were common in the Early and High Medieval periods, to round out the representation of the whole era.
The Great Helm that you listed is an example of a helmet from the High Medieval period (c. AD 1000 - 1250). It became popular amongst Western knights during the time of the Crusades.
The Kettle Helm was also a popular helm amongst Europeans during the High and Late Medieval periods. It probably had its origins in Medieval Byzantium, and spread to the rest of Europe in the 11th Century.
The Spangenhelm was arguably the most popular helmet of the Early Medieval Period. It had its origins in the Middle East and became used throughout Europe during the 6th - 10th Centuries. A variant of this helm is the iconic Viking spectacle helm, used by (unsurprisingly) Vikings, the Rus', and Varangians.
The Norman-type helm, noted for its prominent nasal bar, and based on the spangenhelm, was used extensively during the 10th through 12th Centuries by not only the Normans, but also their various neighbors. Some knights later adopted a menacing faceplate, which hid the entire face, leaving only the eyes exposed. This was similar to the manner in which Byzantine heavy infantry and cavalry of the 10th -15th centuries covered their faces with mail masks to intimidate their enemies in battle.
I'd say this isn't really an answerable question. Every design is a tradeoff between coverage/protection and mobility/comfort. Is a greathelm more protective than a kettlehelm in close combat? Yes, but it also restricts your vision and hearing, and undoubtedly isn't great to have on your head on a hot day or bright sun.
Is the person wearing it an archer? Pikeman? Heavy cavalry? Light cavalry? Are they more concerned about projectiles, or close combat?
Did they supply their gear from personal resources, or was it produced en masse by a royal/municipal armory? What was the quality of metal they had to work with?
More importantly, what can your character afford? Some of these designs require a master craftsman working for days, some designs could be bashed out by a village blacksmith out of a scrap cooking pot.
Further, more important than any possible part of the design is the quality of the materials. Until relatively recently in history, quality, uniform metal was the exception and not the rule. You could have the most brilliant design possible, made by an artisan with a lifetime of experience, but oh shit, here's a slag inclusion, a poor weld or a brittle spot and one day your helmet cracks and you're dead.
Answering your question would be like answering 'what is the tastiest dish'. Depends on your personal taste and what you can afford.
