Not in terms of gore or violence, but an unsettling, eerie atmosphere. Stylistically, I'd like to see them aim for the darker side of the spectrum. Just a handful of cleverly designed "sequence breaks" and/or "advanced techniques" is all it would take to incorporate this element to the game. Metroid, Super Metroid, and Metroid Zero Mission, while all featuring item gating, nevertheless give the player a sense of agency in where to go, and create a very compelling illusion that they are non-linear even when they aren't. However, I think hand-holding should be minimal, a few items should be fully optional to acquire, and the progression should avoid being a simplistic A > B > C > D etc. Not fully open world, as acquiring items to open up new areas and a degree of backtracking is fundamental to the series's core. I'd like to see them attempt to implement some non-linear design into game as well. As Retro has achieved in the past, I want to see a complex and intricate level design woven through a visually stunning worlds that blend natural beauty and futuristic technology, I want to experience the sensation of exploring both desolate and extreme (extreme cold, extreme hot, under the lava, under the ice deep in an ocean. I want varied environments that feel truly alien and defy convention and cliche. My biggest hope is for fantastic new environments to explore. Where I want to see innovation is at the level of content (new environments, enemies, power-ups etc.)
This is a game that needs to deliver to resurrect the franchise. Since there has been such a huge lapse of time since the last entry, I think they can afford to err on the side of caution. On the other hand, I do hope they keep the same basic game-play foundation (controls, first person adventure genre, general concepts). I do not want a continuation of the Metroid Prime story or anything to do with Dark Samus.
My first hope is that Metroid Prime 4 is a placeholder name only.