Answer:
It depends on whether you and Joe are the subject or the object. In general, you would put Joe first and me or I second. If you leave Joe out, it will probably be easier to see whether you should use "me" or "I".
Subject: Joe and I look forward to your visit. You would say "I look forward to your visit", so that is why you say "Joe and I".
Object: This has made Joe and me very happy. You would say "This has made me very happy", so that is why you say "Joe and me".