Best 12v battery solution
Li-Ion have a significant advantage over Lead-Acid batteries for power-to-weight ratio.  You may also be able to get better efficiency out of your (undisclosed voltage) laptop PSU with some series connection of Li-Ion cells closer to the charging voltage. 

With the rising popularity of Li-Ion cells available, there are also a wide variety of charging modules which you can build into your gadget. They will provide proper charging as well as discharge protection.

Ref: https://en.wikipedia.org/wiki/Power-to-weight_ratio#.28Closed_cell.29_batteries