Order of writing variables at the top left of a K-Map
It doesn't matter how you choose to label your K-map. If you are consistent with how you use the mapping, that is, don't change the axis labels between putting your terms in and reading your terms out, then you'll get the same answer.

The K-map is merely a 2D representation (which is easy to see and manipulate) of a higher dimensional space, in this case 4 dimensions (which I personally cannot visualise as easily). The labels have no meaning in themselves, they are merely book-keeping, as long as their use is consistent.

Make sure you are comparing like with like. There is no unique solution to a reduction like this, though there are 4 unique combinations of 0/1 minterm/maxterm, and several other unique 'min this' or 'min that' versions. 

As the map is non-symmetric about the diagonal, and as you say you've reached a solution that's a diagonal flip different from the book, it sounds like, without the need for me to work through your example in detail, that you've managed to slip up somewhere in your placement or readout of terms.