I've never published edge projects to the web before.
Sorted the web settings out to what I need but wondering but do I need to upload the whole edge project file (with the edge project, edge includes etc) or just the publish folder?
The contents of the publish folder is all what is needed to deploy.
PS: the publish folder might have two directories, 'Web' and '.oam', depending on your publish settings. For publishing projects to Web, You only need (all the) contents of the 'Web' directory. If you have uncheked the CDN option in publish settings, then edge_includes directory will be available in Published content.
I hope that answered your query.