Learning the order of the Greek alphabet can be tricky. The way I did it (and the way that most people I know have done it) is to instead learn the places where it diverges from the Latin alphabet in the modern form that is already familiar to readers of English and other Western European languages. This has the advantage, first of all, that one does not need to relearn things one already knows (because the alphabets are ordered very similarly), and, secondly, even what is new has something to attach itself to. But at least for me, that process was rather haphazard, and often performed on-the-fly while looking up words in dictionaries. In order to be a bit more systematic about things, I’ve constructed a spreadsheet to show the correspondences and divergences between the alphabets, along with a brief (and often overly simplistic) discussion of the historical reasons for those divergences. This is very much a work in progress: I would appreciate your corrections, suggestions, and requests for clarification.
The spreadsheet is available on my resources page, or you can access it right here.