I have used Minky and similar products with no problem... personally I didn't notice any huge mess with the cutting, but I use my kitchen counter for cutting and it gets wiped often.
I usually tape my backing to the floor, layer my 100% cotton batting on that, then the cotton top. Smooth and pin about a "fist" width ... I quilt with 100% cotton 40 or 50 wt thread and usually straight lines with my walking foot. Just remember to go at a slow and steady pace, rather than a race because the feed dogs need to move everything along at the same time
