Now that Microsoft has the Xbox One announcement out of the way, it's pretty much a given that the Halo property will be coming to the new platform, and chances are it's going to happen sooner rather than later.
So here are the possibilities for the next Halo installment on Xbox One:
Halo 5. 343 Industries' chance to redeem itself and fix everything that made Halo 4 such an imperfect game.
Rationale: It simply hasn't been long enough since Halo 4 to get a sequel any time soon. Microsoft will likely continue milking this game with DLC (none of which will probably be worthwhile) to get maximum return on its investment.
Original Halo game. Something that will be set in the Halo universe but will either be non-canonical or use an alternate gameplay or belong to a non-FPS genre, similar to Reach or Halo Wars.
Rationale: It would be a significant investment to create a brand new game based on Halo, especially if you want it to run on new Xbox One architecture. However, because expectations for non-canonical games are not as high as for direct sequels, Microsoft could farm it out to a third party for relatively cheap and see what they can do with it.
HD Remake. It worked wonders for Halo CE and the Xbox 360, and it would do the same for Xbox One.
Rationale: HD remakes are tedious to make but most of the work is technical, not creative. This is a perfect project to assign to a studio that has a lot of programming savvy but no real superstar experience in the creative department. By working hard and putting a lot of overtime hours into upgrading models, making new textures, and replicating physics, they could make a blockbuster title for the new console without taking a lot of risks.
My conclusion is that the first Halo game on Xbox One will be a Halo 2 Remake. It is the next in line, the logical choice, and the cheapest to make. Microsoft knows that Halo is its hottest franchise and will undoubtedly use it to promote the new system. I expect development to be in early stages and the release will be scheduled for the slowest part of the year for gaming. So expect Halo 2 on Xbox One in the summer of 2014.