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The core ROS libraries will run on just about anything, particularly if it can run Ubuntu.
Which packages you want to use and what you want to do with your robot will have a much more significant impact on the CPU and memory requirements.
As suggested elsewhere (http://answers.ros.org/question/203712/to-buy-laptop-for-ros/ , http://answers.ros.org/question/61748/laptop-recommendations/ and http://answers.ros.org/question/52679/laptop-recommendation/ ), look for a laptop with an Nvidia graphics card.
Given your extremely limited budget, just buy the most powerful laptop you can, and hope it's enough.