There is a big difference between the iPod nano and the iPod touch. The iPod nano is based on a flash drive which is not affected by vibration, so you can strap it to your arm and take it running anywhere. However, the iPod touch (like the iPod classic) is based on a miniature hard drive which IS affected by vibration. If you take it running, the hard drive will quickly "park" itself to protect itself from damage. In other words, it will keep shutting itself off and will require continual resets. The only exception is if you run on a treadmill where you can prop the iPod touch on a stationary surface.
So, two reasonable options: either (a) get an iPod nano, or (b) get an iPod touch if you want/need the larger screen and larger memory, and then get an iPod shuffle (which is flash drive based, like the nano) for running.