I'm not acquainted with the distinctions between types of armets that you outline - wedge and pointed, so I'll leave those aside.

I'll start off by challenging your assumptions a -bit-. Armour's form isn't simiply a case of picking and choosing what's the most 'optimized' harness with the best 'specs' for the task - as say, an English Knight in 1470 your choices aren't going to be unaffected by fashion, both what's current at that time and by what's popular in your area. You too would be a creature of your own time and place, and would make decisions that were conditioned in the same way that people around you did. Which is to say, you would be unlikely to select a helmet that was completely unknown to your time or place - instead your possible choices would be shaped by fashion. This is not to say that people didn't make choices within that framework, or even adopt the fashions of neighboring countries, but these choices were limited by where and when they lived.

So with that said, let's assume that you're in a place that has a variety of helmet types in fashion. Let's say Spain - here we see kettle hats (called cabacete in Spanish), armets and sallets serving side by side, though some are more popular on different parts of the Peninsula. Let's assume that year is around 1470 through 1492. This means that some types of helmets, like the Great Bascinet, are out of fashion except for use in tournaments. Let's also assume that in all cases we are talking about warfare rather than tournaments or judicial combats.

First off, naval combat. I have yet to see any special 'naval' equipment that is distinct from the equipment of normal soldiers, and equipping naval expeditions actually shows up in our documentary records several times. If anything, naval combatants are fitted with an overall lighter armour, judging by the Howard accounts from 15th century England. But there's no mention I have seen of a helmet 'for sea service' comparable to later specialized naval weaponry.

For fighting on horseback, one of the best helmets out there for you will be the armet. Equipped with a wrapper around the front it will present two layers of 2mm steel and a prow-shaped profile for your oppenent's lance to glance off of. Equippedwith a brow reinforcement over your forehead, there really won't be a front-on weakness other than your eyeslit, and there's only so much you can do with that.

For fighting on foot, I would recommend a cabacete. Other people in Europe call it an 'iron hat', and later people will call it a 'kettle hat', but you don't know that yet. It offers fantastic vision, full movement of your head, and protects you pretty well, especially when equipped with a bevor/buffe, which can be raised or lowered to protect your face.

But what about sallets, and the early sallet close helmets that are just appearing in the 1470's and later? These are great all-round helmets. They can serve on horseback or on foot, and the attached, pivotted bevor of the sallet close helmet means that gaps are less likely to open between your bevor and visor at inopportune times. This 'all round' appear has made these helmets the most popular in Europe for a reason.