There is no 'official' acronym for MBF

I use MBF, as you may have just noticed, simply as it is short and to the point.
If you want to start with A Song of Ice and Fire then the most straightforward way is to pick up A Game of Thrones (Book 1) and read on from there. There are two prequel short stories, The Hedge Knight and The Sworn Sword, which can be read without prior knowledge of the series, but they take place 90 years before the books and only have a minor impact on the 'big' story in the novels. Neither of them have any magical elements in them at all. By the time you do start reading in the autumn, we should have (fingers crossed) the fifth novel either out or about to come out, and definitely the third short story as well.
As for the level of magic in ASoIF: probably slightly higher than in Lord of the Rings. You have magical or semi-magical creatures, such as basilisks, manticores and obviously dragons, although they are rare, and a low level of spellcasting, mostly restricted to just two or three characters. There's also certain structures (The Wall, Storm's End, Dragonstone) which were built with magic and at least one place (Harrenhal) that is cursed somehow. I'd put the amount of magic in the series at about 5% of MBF, if that.
As for the no-magic version of ASoIF, I think GRRM mentioned that the direwolf scene that he first came up with could be read as a portent of things to come or just one of those weird coincidences that crop up in life (like a guy writing a novel about the biggest ocean liner ever which was sent to sea without enough lifeboats that hit a iceberg and went down with over 1,000 deaths...and publishing it in 1896 and calling the ship 'Titan'). He still won't elaborate on it being some kind of mystical happening or pure chance. The direwolves themselves aren't mystical as they really existed, I think in Iceland and Scandanavia hundreds of years ago.