I don't use a fan, but I have wired up a few lights. I went the easy route and found a small 12v battery. The type I have was out of a Verizon Fios box.
http://www.batterymart.com/p-12v-7a...m_medium=CPC&gclid=CMrO6-Xt3a4CFQ2FhwodmFnKYA
I recharge it with a trickle charger in about a half an hour. It will keep a charge for months. Its small, cheap and easy.
If you look close under the edge of the top. Those are live well lights . I made brackets and they shine down on the tailgate, where I usually end up cooking. I have another light that shines into the shell. That one I made out of leds myself. You can get a big bag of them pretty cheap. A piece of breadboard, a resister and some solder and you can make them how ever your want. The battery is in the box, along with tools, hatchet, etc. Those dual battery set ups are cool, but they are bulky and spendy. I don't use a fridge so it seems a bit overkill to me.