I wrote to Target and asked them to make it a policy for their employees to always ask the customer if they want a bag when they're buying just one or two items. They gave me what I consider a very lame excuse, that some people have difficulty carrying one or two items without a bag. So instead of those people asking to get a bag, I have to ask to not get one. It would work out the same, except most people who don't need one don't bother to ask for no bag, so there's a lot of waste. Now when they say "hello" to me and I have only an armful of items, I say, "Hello. No bag, please." That way, they don't sneak my stuff into a bag while I'm paying or something.
As for paper or plastic, I get almost all paper, because I use more of them, and they also decompose much more quickly than the plastic bags I see littering the roadsides everywhere.