I like the random effect of the paper bag method, but I found that my pieces would get creased and some wouldn't lay flat when I tried to sew them.
These days as I am cutting for a scrappy project, I deal out pieces into 5 or 7 piles like they were a hand of cards. Each pile then will get cut a few times and then stacked altogether. This gives me a fairly random order from which to pick fabrics but the pieces still lay flat.