For a laptop with the best power solution, look for Centrino setups. This uses a processor (Mobile Pentium-M) and chipset optimised for low power consumption, but with plenth of processing power.
Laptops wth Celerom-M (the mobile version) are less good in speed and power management, but provide very low cost.
So basically you have a choice. A very cheap Celerom-M laptop with a spare battery may also be a good solution.