expect that 5v will probably be enough in the end
5v is the voltage and is not a limiting factor - in fact you will most likely want 5v. What would not be enough would be current, such as in the case of trying to run too many LEDs from the regulator on your arduino board or worse through pins.
If you want to wear the helmet then you will need to run on a battery. You could use a good sized but fairly expensive lithium ion battery pack for an iPOD as long as it has 1.2amps (1200ma) or higher output. The plus with this setup is it is small and can be used to charge your phone / ipod, etc - when not wearing the helmet.
When you are running on non-battery power - you will still need an external power source. If you are running 60 leds then that need 20ma each will be 1.2 amps. This is more than you want to run from either your arduino regulator or the USB provided power so you will need external power - a DLink 5v power supply is a commonly used item for external power.
As for how you do this electronically - I stopped soldering chips or using 595/TLC chips a while back so I'll leave the chip selection / wiring assistance for people that more into that aspect of your project. I assume you don't want to "cheat" and use a pre-soldered solution with chips built in .. because that would be no challenge at all and you won't learn much in the way of electronics.
Best of luck.