The ULN2803 is a great chip and is quite useful but it won't be able to run more than 3ft of 12v rope light per channel (500mA/Ch) you have 8 on the ULN2803 and you can combine more then one channel to increase the output if needed
the nice thing is it is easy to wire just feed the inputs from the arduino output pins and the GND pin from the 12v supply and the arduino GND then connect the outputs to the (-) on your lights and the 12v + to the (+) on the lights