The main question I have is whether this a battery that is good for the fifty dollar robot: http://www.all-battery.com/6v2000mahnimhsidebysiderxreceiverbatterypackswhitecconnector11106.aspx
Yes, as long as you pay attention to the voltage, as the controller won't handle more than 5V.
I'm somewhat confused as to the meaning of mAh, even after reading the tutorial. mAh
is a measure of the capacity of a battery.
Assuming for a minute that the world is perfect, your 2000 mAh (2Ah) will supply 2000 mA
for 1 h
our (mA x h = mAh), 1000 mA for 2 hours or 4000 mA for half an hour.
In real life it won't however, as the capacity measure is set to 5 times the 5 hour discharge current, so the 2000 mAh battery will give 400 mA for 5 hours.
Drawing more current will lower the usable capacity, so a 2000 mA draw may only last 45 minutes (or whatever) and with a lower current draw, the apparent capacity will be higher.