How to select headphones that can be driven by an old iPod?

My iPod Video is 14 years old. I understand some headphones can't be driven by an iPod because the sound would be too low, even with the volume cranked, and some headphones sound better with DACs. A DAC wouldn't work with my iPod.

Not certain it matches your referenced model but some measurements of the "5th Gen" iPod show it capable of producing 1.4V before clipping and having roughly an 11 ohm output impedance. This isn't too bad on power but the output impedance will be problematic for some headphones. If I were trying to match headphones to that device I would look for something with an efficiency greater than 100db/mW and at 80 ohms or higher nominal impedance. An efficient planar headphone might work, as would some single driver IEM's. Any multi-driver in-ear headphone or headphone below 80 ohms may be altered by that output impedance, it's not a very low value which allows more flexibility in pairing. Any particular reason you are set on remaining with the iPod? For a lot of headphones an iPhone would be a easier source to pair if portable listening is your goal.
May 18, 2020
I realize the iPod is old and likely won't last another 14 years, so I've decided to eventually a Sennheiser 6XX and buy something like a Schit Magni/Modi stack and listen from my computer. Whenever the iPod dies, I'll buy a new one and use something like a Dragonfly DAC.
May 12, 2020
Might be time for an upgrade--to a newer iPhone. More storage, better sound--and you can call your mom for Mother's Day.