I have hundreds (and hundreds) of dies from every company you can think of. The only dies I would not use with fabric are the very thin 'wafter' dies, for instance Sizzlets. A crisp fabric will always cut better, so starching is a good idea. I would only cut one layer of fabric with the Bigz/Originals, especially if the die has a lot of detail. If the fabric is not cutting well, put a piece of copy paper on top of the fabric. Fabric goes next to the blade then the paper then the cutting pad. Different brands of dies may be slightly different thicknesses, so you may need a shim. Oh, and one last thought, many of the Bigz/Originals die designs have perf blades to enhance the design. Here is an example:
http://www.sizzix.com/outlet?&page=1...18&w=originals
Go to the leaf design#654999, then look at the "line" image. The leaves have veins made by a perforated cut. These will make little cuts in your fabric on these lines. A shape like this should be fused entirely down and the veins should be satin stitched, if not and the item is laundered a lot, it may begin to fray along these lines. Let me know if you have any more questions.