Sorry one last link
These are the ones that I am looking at.
http://www.beepscom.com/category_s/355.htm
40 amphour ones for the Kart and 200 amphour ones for the car.
Hey I am thinking of using some Lithium too.
I would stay away from the Thundersky batteries though. There is no U.S. (sorry assuming that you are from the U.S.). I belong to an Electric Car mailing list anf there was a group by of the Thundersky. Half of the batteries were no good.
As for...
Those three spead switches for fans are only designed for 15 amps. And for AC instead of DC. AC is a lot easier to switch on and off than DC.
What you are trying to get is basicaly called a contactor controler. These were often used in anything that needed multiple speeds before cheap PWM...
That kit that you listed should work but you are not going to get anywhere near 10 mph with that. That is designed to drive a 20# scooter at 10 - 15 mph when loaded with a 100# kid. To keep from overloading it you will need to gear it down quite a bit.
The controller will cut off when the voltage drops below a set voltage not a set amps.
If you want to keep an eye on the amps while you are driving it I suggest that you install an AMP meter.
Search ebay for DC Shunt AMP meter. Found tons of them when I did a test search just now.
Basicaly...