A city bike or comfort bike would serve you well - a city bike can include Dutch style bikes like the KHS, or even beach cruisers with a 5 speed hub. I'd recommend a 5 speed hub, having used one living car-free in New Orleans for a year... it's got enough gearing to get you up short steep hills, or long shallow ones, and you'll find yourself shifting into higher and higher gears on the flats as you get more in shape.

While I have no doubt someone, somewhere, makes an insulated pannier, it would be a lot more economical just to buy a re-usable insulated shopping bag or two from the grocery store or HugeMart, and stuff that into a pannier.