The main difference between the Lilypad Arduino and the Lilypad Simple Board is that the Simple Board does not have Rx/Tx pins (receive/transmit), which are typically used in wireless communication -- for example if you were integrating a Lilypad Xbee board to your design. I believe it has less IO pins as well, if I am remembering correctly. So yes, using a Simple Board for your project should be fine.
The FTDI cable is essentially the same as the breakout board, and yes you can use this to program the board from your computer.
Given the number of LEDs you plan to use and the required power source, you will need to be using a transistor(s) on your banks of LEDs. A TIP120 will probably do the trick. Consider wiring them in Series/Parallel arrays, as used in LED matrices. Consider also that conductive thread is quite resistive. I always like to incorporate iron-on conductive fabric wherever possible, since resistance does not diminish over distance as with thread. I cut strips of conductive fabric and then join them to components using a few looping stitches of conductive thread.