It's a good idea to have a dummy student account so you can see how things work from the student perspective. Set up the online assignment as teacher. Then login as your dummy student and click on the assignment activity to see what happens next.
An online assignment is appropriate when you want the student to complete the assignment in one sitting. For example, many people are now forced to use it as a replacement for the denigrated Journal entry. It can also be used like an essay question on a test. If you want to give students more time, choose upload
or offline assignment.
An offline activity is really just a resource, like a Web page or a file. Students read it to see what you want them to do, and then do the work completely outside of Moodle. They do not even submit their work through Moodle. For example, they may hand in their work on paper. The only value that Moodle adds is leaving a place in the gradebook for a manually-entered grade.