Finally. A thread we can get our teeth into!
I usually take leftovers. I don't put plastic in a microwave so, if something needs to be heated, it goes into a glass container (with the proper lid). Anything else is good in plastic containers or ziploc baggies. I've not had a problem with spills. I take my lunch in a soft sided cooler that I hang on the side of my rear rack with a combination of a carabiner clip and hd wire tie. I used to hang it on the handlebars but have come to like this method much better.

Packing for 3 meals as the op and others mentioned would require a slightly larger cooler than I am presently using. It would not be a problem to hang it the same way.