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I highly recommend this case. I bought it at the Microsoft Store, also as a part of the bundle. It was $35 otherwise. It's made by Incipio. The outside looks like burlap but it is protected by a "wax coating" that prevents tearing. The inside has faux fur that will not scratch your Surface. It is very lightweight.
The zipper opens from the top (long side) or from the side (short side) so whether you have a horizontal or vertical bag, it's easy to get the Surface out of this.
There is only one pocket aside from the main storage area. I took the photo above with my surface, but the pocket you see there currently has the Surface Pro 3 charging brick and cable, the SP3 Pen, and the Arc Touch Mouse Surface Edition inside it. You can barely even tell that there's anything in the case.
The Microsoft Store had the beige one that I have, as well as Grey and Military Green colored ones.
Only complaint is that there's no handles, but this is really meant as protection and storage rather than a carry bag.
How snug is the fit? The case is likely not "made for Surface".