NiMH- non-toxic and charges faster with higher capacities (but higher internal resistance than NiCds, but usually an extra cell is added on to compensate).
The battery you use is often limited by how much money you have to get the battery (and the charger). Don't even worry about battery brand- changes are you have zero choice.
The current the motor will use in normal operation is dictated by voltage, wheel size, weight, maximum incline encountered, motor torque, motor speed, and gear reduction.
But to get worst case, you must find the stall current of the motor which has nothing to do with the robot. Take your motor and clamp the shaft. Momentarily apply power to it and measure the current. That is your worst case current for that motor. THis will not tell you if the motor is strong enough to drive your robot though- just the worst case current the motor will draw.