What is the cost of converting 12V (lead acid battery) to 220V and back again to power 12V appliances?
You can estimate this fairly easily using 
$$ P_\text{IN} = \frac {P_\text{OUT}}{\text{Eff.}} $$ 
for each device. So, let's say a sine inverter has an efficiency of 75% (I didn't look this up) and the mains to DC converter has an efficiency of 85% then the power required for a 12 V device powered on mains rather than directly will be
$$ P_\text{IN} = \frac {P_\text{OUT}}{\text{Eff.}_1 \times \text{Eff.}_2} = \frac {P_\text{OUT}}{0.75 \times 0.85} = 1.57 P_\text{IN}$$  

I've never had to do this but I would be inclined to use DC where possible. That way you have no losses for the 12 V devices and one conversion loss for each of the others.