I use a rotary cutter and acrylic ruler for patchwork pieces, and for cutting a strip of binding, bias or straight, but for cutting out garment patterns then it's shears and scissors (Fiskars shears for the lighter fabrics and Ernest Wright scissors for the heavier stuff).
I do use pins, the type with a bobble end - glass is better than plastic if they happen to come into contact with a hot iron! If it's a delicate fabric I try to keep them within the seam allowance, but honestly I can't see how the pattern doesn't move around if it's not pinned down. The other advantage of pinning is that each piece stays with it's pattern piece until you are ready to use it. A pile of cut put pieces of fabric with loose cut out pattern pieces is, IMO, just asking to get muddled up.