Once you complete my course, the next thing you should do is figure out how to program your mouse to make a speed run. That is, figure out how to make your mouse return to the starting cell and then travel to the target cell as fast as possible using the best route without stopping. After that, you're ready for a faster mouse. I highly recommend the design worked out by Jasper Holton using the 2wd miniQ Robot chassis and encoders from DFRobot (although I would spring for some standoffs and the Upper Deck for miniQ so that I could wire everything together on a single short breadboard). To program Jasper's robot, you will have to learn to use an H-Bridge Motor Driver as well as encoders and interrupts (see below).
Upgrading the Voltage Regulator
Below is an example circuit that takes input from a potentiometer and transforms it into a digital signal using the comparator which is then fed into pin 2 (which is interrupt 0). The two 10K ohm resistors are used to create a reference voltage. The 3rd resistor (in this case 100K ohms) helps to adjust the hystereis to minimize debouncing. I should have added a 4th resistor between VINA+ and the potentiometer (in place of the yellow wire). Page 12 of the datasheet describes how the ratio between those resistors would change the trip voltage. To use this circuit with your mouse, simply replace the analog readings provided by the potentiometer with what you get from the line sensor.
The Parallax Mouse Sensor Library - An Alternative to Encoders
One way to keep track of how far your robot travels would be to strap a mouse sensor to the bottom of it. Parallax sold a mouse sensor kit (#28560), but they didn't provide Arduino code for it. That's where the ParallaxMouseSensor library comes in. To use it, the mouse sensor must be set up for the Advanced Three-wire Connection. After that, it's pretty simple--see the example code in the library (available below) once you drop it in your Arduino folder's library folder.