Well; you sort of answered your own question already. The Brodie style helmet went out of fashion and the stahlhelm type stuck. They were both developed as a way to reduce death from shrapnel in the trenches, which is why the British one has what is perceived as a wide brim (it's really not that much wider, it mostly just looks like it because of the shape) - a lot of the shrapnel came from airburst artillery. As warfare developed during and after WWII, the helmet that was the most designed for trench warfare disappeared in favour of something a bit more sleek and covering of the back of the skull such as the M1.

Nowadays, most modern fighting forces use a lightweight helmet system made from kevlar/aramid and plastics instead of steel helmets, but the shape is still very similar and some function has been added, such as the opportunity to affix night vision systems or similar gadgets.

Is it against the rules to ask for some historically accurate pictures of these helmets? I tried on Google, but I don't know which are accurate.

This is actually not as simple as it seems. The stahlhelm definitely has a better shell, its general design is still being used today, as you mentioned. The thing about helmets is that they protect the head, so you don't want little bits of debris going through it, but your head also really doesn't like impacts, so you want to mitigate them as much as possible. This is the liner for the stahlhelm. I wouldn't want to have debris with any significant heft to it hit my helmet with that padding. If something were to dent your helmet where your forehead was, you would have a little more than a headache.

As mentioned before the Brodie style helmet was not that effective of a design because it sits so high on the head and doesn't cover as much of the head as any other helmet of ww2. It does have slight padding, and the mk 4 turtle shell also addresses the cover issue of the brodie with a similar liner.

Another thing to note is paratrooper helmets. Para helmets needed to protect the head from large forces, like slamming your head against the ground after, you know, falling out of an airplane. This is a Mk 3 para helmet liner used by the Commonwealth. unfortunately it didn't give as much protection, as the helmet stopped just about at the ear. The fallschirmjäger helmet was also padded, but removed the rims that make the stahlhelm so good at protecting the head from shrapnel.

The M1 is a compromise between coverage and padding, However it was a one size fits all, so if you have a melon head you wouldn't have the space between the helmet as the guy with a small head. Also The American paratrooper helmet had very few modifications from the M1, which could either be a testament to it's design, or just the nature of wartime production. I unfortunately don't know very much about Italian, French, Japanese, or Russian helmets :( If I had to pick a helmet, and if i didn't have a melon head, I would pick an M1.