Anyone who knows much about the history of occult practices worldwide will tell you that magic is often connected with religion in some way. For instance, the Medieval grimoires that form the basis of much of the hermetic practice that Neal has been writing about are generally attributed to biblical authors (e.g. the Key of Solomon and the Lesser Key of Solomon, the Sixth and Seventh Books of Moses, etc), and a number of those that aren’t still emphasize the importance of Godly practice and righteousness (e.g. the Book of Abramelin the Mage). In primal or tribal religions magic and worship are generally indistinguishable from one another, and magical practices are a common part of Eastern religions (e.g. Buddhism, Taoism, Shintoism, etc).
However, in speculative fiction the arcane and the divine are often, but not always, separated (Ursula Le Guin’s Earthsea, Dungeons and Dragons, The Dresden Files, The Mercy Thompson Series, Shadowrun, etc). Sometimes the magic of the divine and the magic of the arcane are at odds, and in other cases only one is a true source of magical power. As an author something that you’ll have to consider is how the divine powers and the scientific forces of magic will interact in your world.
If you want your world to particularly reflect the historic practices of magic then it is obviously best to focus on connecting your magical practices with the religions of your world. As the writers at Megalith Games pointed out in their interview, it isn’t difficult to take the general ideas underlying magical systems from history (such as Qabbalah, or Shamanism) and alter them for your own world. Using these historic systems provides a foundation upon which you can build your own ideas, and it also gives you magical system, and perhaps your culture as a while a connection to the real world. This approach also gives you the room to express your own creativity in fleshing out these magical systems. While the foundation comes from elsewhere (and takes a little research), the details of how the magic works, what can be done, and how it is done are all up to you.
Of course, you may also want to develop religious magical systems that have no connection with the real world. In this case you need to develop the foundations of the magical system, which I’ve discussed earlier, and then build your system from there. Remember, in writing (as in everything) the foundations come first.
On the other hand, if you want to build arcane magical systems that have no connection to religion, then hermetic magic is a good place to start. While hermetic magic often does have a connection to religion, that connection is often tenuous at best. This is because the Christian church generally disapproved of magic (with the exception of exorcism: Roman Catholic exorcism rituals bear a strong resemblance to the goetic practices of the time), and some magic the church openly suppressed (predominately magical practices having to do with summoning, controlling, or communicating with angelic/demonic beings or the dead, and magic having to do with divination, along with the majority of low magic that drew heavily from the pagan religions of Europe).
While much of the Hermetic canon draws upon the authority of scriptural figures, or emphasizes the importance of God, it is also highly ritualized. While you will still need to build your own foundation for magic that draws its power from non-divine forces, the ritualistic structure of Hermetic magic will give you a number of good models on which to develop your own systems.
Broken Mirrors 
You’ve clearly put a lot of thought into applying real-world histories and cultures to the creation of your fantasy. Very interesting post!