Which should I use, a blog, forum, discussion, chat, wiki, assignment, or quiz?

Blog, forum, discussion, chat, wiki, assignment, or quiz?
Depending on the nature of the course and the specific activity, one of these activities will be better than the others in meeting your goals.

The author of a blog is the only one who can edit or comment on the blog. By default, everyone with an Eckerd College email account who logs into the Course Materials site (not just members of the class) can read everything posted in the blog. I don't recommend making frequent use of the blog.
Forum and Discussion:
The Moodle word for a Discussion is a Forum so these two are essentially the same. (Technically, a Forum can have several Discussions or be limited to just one discussion.) There are several different settings for a forum and these are set by the teacher. A forum will have one or more topics (discussions) with one or more responses per topic. No one can change the responses that have been entered, and (usually) everyone in the class can see all the topics and all the responses. The responses are nested below each topic.
One nice feature about a Forum is that it allows students (teachers) to enter a file/document as part of the response. Thus, a Forum is a good way to allow students in the class to see work done by other students. Any kind of document can be entered, including images and small audio files. Only one can be entered per comment, but a person can enter several comments if they wish, each with its own attached file.
Settings for a Forum can be chosen so that an email message is generated every time there is an entry in a Forum. This should be used with care to avoid creating too many email messages.
A chat is a series of responses or comments. Those participating in a chat are usually on-line while the chat is going on, while people participating in a Forum (Discussion) often will be away from their computers for hours or even days. The chat entries will be listed chronologically even if the comments are referring to different topics. A chat is designed for synchronous interaction while a Forum is designed for asynchronous interaction.
A Wiki is designed to be a document where several people can collaborate. The teacher and students can add material. In addition, each person can edit or delete or rearrange material entered by anyone. If the editing is restricted to a group of students, the teacher can still use a setting that allows everyone to see the edited document. The teacher can see all versions of the document and a history of who entered or edited what.
Only the teacher can see the comments and/or attached files that a student enters in an assignment.
A quiz consists of one or more questions that a student answers. Usually the student cannot submit an attached file. Only the teacher can see the answers that each student gives to the questions.