Are you looking for a one time import / nightly / full integration where editors actually can see instant changes on other site.
Do you need editors in EPiServer to be able to edit content on other site?
Most likely full integration.
I would probably go on the content provider track then. There is also a Rest service API you can use but it's not very well documented. Building a scheduled job in EPiServer that gets stuff from umbraco and using default content repository is not a bad option either.
I am new to episerver and I would was wondering what would be the most sensible way of integrating with a 3rd party CMS system (umbraco)?
Would the Content Channel be a sensible route to publish the content into EpiServer CMS or Custom Page Providers (If these still apply) or is there another way?