Shop Green

Simply placing your produce in your shopping cart will not hurt it.  Presumably you wash it when you get home anyways, so what's the difference?  If you don't want your apples rolling around, place a shopping basket in the cart, and put your produce in that!  Alternatively, Marie Naubert has come up with the wonderful Moukisacs, which are resuable mesh bags that can not only be used for produce but also for bulk foods, like nuts and lentils.
If you live in an area that allows you to choose between paper, or plastic, choose paper.  Yes, paper bags are a product of forestry, but most forestry is sustainable in North America and the paper is recyclable, wheras the plastic will end up in landfills.  If paper isn't an option, bring your own reusable bags when you go shopping, such as the BYOB (bring your own bag) line of reusable shopping bags (they also make for great totes, and they're costomizable).
As far as milk goes, paper milk cartons are recyclable, and you might be surprised to know that some in areas in Canada and the US, you can still use refillable glass milk bottles.  Do not use glass bottles for your milk if they aren't refillable because they're energy hogs.  Those big jugs of milk in the thick plastic are also recyclable, but plastic milk bags make for nasty landfill.
Meat is easy: buy it at the deli or at your grocery store's deli counter.  Tell them what cut you want, and they'll wrap it in paper for you.  No plastic to speak of!