When using Office 365 APIs to access only email items, should I use the Graph API or Outlook API? I don't need all the different services that the Graph API provides, but the Outlook API seems more full-featured. Which one is more future-proof?
I would actually suggest using the Graph API if it has the features that you need, simply because the fact that you do not need anything outside of Outlook now, you might in the near future seeing as different Office 365 features are starting to get more and more integrated with each other. Next to that, I personally think it is better documented and overall nicer to work with. As an added benefit, if you'd ever develop another O365 related integration you already know how it works, as all services in the Microsoft Graph use more or less the same structures.
If you're after the most widely supported solution try the EWS API as most Exchange servers (even those not in O365) will have it enabled and Outlook gives you a token and details for that as well. It is not the most future proof however.