I have used the hl1606 you mention and don't like it much. You can't just tell the chip, "go to this color" like you can the lpd6803 or the ws2801 chips. They are really made to run patterns using a simple controller. Since you have a smart controller, thanks Arduino, I suggest you look for LEDs with the chips lpd6803 (32 steps of PWM built in for 323232=32K colors) or the ws2801 chip (256 steps for 16M colors). This library works pretty good with both chips http://code.google.com/p/fastspi/. If you have already purchased the strips then you can work with them to create some cool effects.
If you plan to create a wearable suit, you need to also consider the time you need it lit and the current needed to run the lights. If you want a portable unit run on batteries, then you will want to test the patterns you are using and also understand the current draw of the lights and specs you are reading on power supplies.
Do you need wireless because only your computer provides the music responsiveness you need, or are you looking to control multiple suits at one time and have them in sync? This can be an important decision point in using wireless transmission or an on board music board.