Yeh it is very hard to pick the right battery, simply because it doesnt exist i think! The properties electric vehicals need are, lightweight, high current, high capacity, and cheap. I think you probably need to increase your budget a bit, and try looking at deep cycle flooded lead acid batteries. I know lots bout batteries and electronics cos i finished my robotics engineering degree last year!
Lower Ahrs mean less range, Ahrs are like a cars fuel tank, less is less distance.