IIS Express or Owin self host (as service)

It is always difficult to say something about this kind of situation because each case is a case and only knowing details is it that gives a reasonable decision. And it's complicated because in general neither who is doing the project knows all the details.

The self-host is interesting in cases you have described. You lose a few things by not using IIS, but it gets lighter and simpler to administer. And what you lose probably will not be necessary in this more controlled scenario.

For all that has been described and from what I have seen of your intention I would think of going from .Net Core using OWIN. Depending on the project cycle I would already try using the ASP.Net vNext which is the new version of the Web API. It's not ready yet, but it's well advanced.

If one day needs to switch to IIS, it's quite simple. At least from a programming point of view it should be almost transparent.

IIS Express is not intended for use in production, so it can even be used, but it's one less reason to use it.

Of course, you will have to learn the whole operation of OWIN / Katana. I think it's worth it in the long run to know this, but if you're in a hurry it's best to use what you already know and do not need to create specific codes. There, in this case, I would go from normal IIS.