Which is the safest side to place a foldable rack-attaching bike basket?
I'm speaking from personal experience here.  Looking at the bicycle from the back.  The drive train is on the right side, and when you use the kickstand it leans to the left.

When I commute to work, I tend to put my messenger bag with rear rack attachments on the left side.  Mostly because the bike is already leaning that way.  Once, when I was getting ready to leave work. I placed the bag on the right, and proceed to begin to tie my pants so they wouldn't get caught in the chain.  The whole bike, bag and all, fell right on top of me.  The incline of that particular part of the parking lot and the weight of the bag were enough to throw the whole bike of balance and rendered the kickstand useless.

Since then, I've always put my bag on the left side.  The idea of my bike falling on the right side and bending or breaking a derailleur just freaks me out since I've yet to learn how to fix them or adjust them.