Original post: Fr.NovumOrganum
There is a lot of overlap between Thelema and the GD. Regardie's fine biography
Eye in the Triangle documents this well. And, you are right, there is nothing that contradictory between them below the veil (5=6/6=5). To be honest, for a starting magickian, it probably doesn't make much difference which you choose, as long as you start to work. The Golden Dawn traditions might even be better for providing a solid elemental balance for a newbie that the oto or the A.A. actually.
There are some great books which lay out the methods of the GD. See, for example, the
Godlen Dawn by Regardie, or one of the self initiation books by the ciceros. Don't worry about the politics between orders. I can say from experience, that the oto and the cicero's GD are not at each other's throats; in fact, at our camp GD'ers are often very welcome guests of honor.
What are you looking for in joining an order? I myself found mail order courses to be cold, so I struck up a solitary practice, with only the occasional wiccan at the occult store to talk to (

). But then I got lucky, in finding two things: my local camp body of the oto, and
these boards. And I mean that. These CM boards are amazing. There are a lot of people here to share experience, give advice and grounding, and just to talk about magick with.
I guess what I'm saying in a rambling way is, yes, just get started with the LBRP, the MP, and the KC. No matter what order you join, if they don't begin by having you master those basics, they are doing you a disservice. And when you do find one that is right for you, you'll be prepared. And remember, we are your community.