A 60lb son running a 2.5hp motor, he'll fly away...
Anyways, if you are using the motor just because you have one, and I don't believe you are looking for the most efficient possible design, just something with some go, running the 130v motor at only 24v or 36v, geared down for the wheels should get you up to a few to 10 miles per hour or so even going up-hill. Again, efficiency will be not horrible, but, don't expect the optimum 82% possible from the motor.
Based on knowledge working with 2 old treadmill motors, if you decide to keep using the mini-ribbed flat belt with the pulley they typically have, the drive RPM running at 5v thru 36v, you can expect a really smooth quiet functionality. Any higher voltage would be too much for a 60lb child unless you are making a racing cart and your child wears appropriate helmet and pads safety gear while your go-cart has re-enforced crash cage and seat-belt. Yes, at the higher voltages closer to 100v, your motor will get close to 80% efficiency, but your power electronics will need to improve to handle the voltage range and have serious safeties in it's design.
As for speed control, I would go the PIC route using the PWM driving a single N-channel-mosfet running from a 24v, or 36v battery setup. I would use an ADC input to read your throttle so you can create a custom curve of throttle position VS PWM % drive + a few outputs to drive a few LEDs to display throttle position. You can get more complex by monitoring battery voltage and compensating...
Warning, the treadmill motor, if it is a good high quality one, will sink a ton of current as you begin from a stopped position. They do generate a lot of torque and you should program you PIC accordingly. IE softly engage the throttle...