From an Adapt perspective, the main thing is to make sure the LMS can cope with responsive content & HTML5. Some Learning Management Systems display the course content using either a frameset (which is not valid HTML5 and therefore can trigger Internet Explorer to drop into compatibility view) or an iframe (which can have problems with responsive content, particularly on iOS).

Assuming you want your content to be available on iOS/Android, you also need to check that the LMS doesn't use Java as that doesn't work on either of those platforms.

SCORM Cloud certainly works fine and I'm pretty sure that any recent versions of Moodle or Totara do too. We have a lot of clients using Cornerstone onDemand and that seems to work very well.