Welcome to the Orthodox Church. In my experience, those who discover Orthodoxy almost invariably convert because its theology, as you have noticed, is so rich and so beautiful. Orthodoxy is considerably different from Roman Catholicism and Anglicanism, so they're not interchangeable. It is worth studying up on Orthodox theology so that you really know the difference.
The conversion process does vary, but the primary activity is regular attendance at church--joining into the life of the church--and study. Some churches have official programs for catechumens and some don't. Since you're in a new location, you might want to visit a couple of different churches to find one you like, and take it from there. Speak to your priest at the earliest opportunity. The site Journey to Orthodoxy
has numerous stories of converting and being a catechumen, which I think you'll find interesting.
Once begun, the process ordinarily takes about a year, but, again, it varies.
Christ is Risen!