Newbee question re controlling LEDs

One issue is that the cable need to be able to be about 15-20 feet long from the computer to the ardunio

So have a short USB to FTI chip lead, then the long lead can be serial. At that distance you might get away with just TTL, otherwise you will need a MAX232 at both ends to boost the signal up to RS232 voltage levels and then back down again for the Arduino.