If you are not happy with the earbuds that came with your iPod or they are missing or damaged, don't worry. I've had an iPod classic for about 2 1/2 years and have tried numerous pairs of headphones with them. I have to say, the iPod is the most headphone friendly device I have ever encoutered. Matter o' fact, I've never heard a pair of headphones/earbuds that sounded less than reasonably good with an iPod.
I currently use a pair of Sony® MDR-X500™ headphones with my iPod. This btw, is one of the very few Sony products worth buying over about the last decade. When I have to go into the city, my boss wants me to park the co. car at the park & ride and take the bus. He buys the bus pass, so okay. It saves him $ on gas & parking, etc. So, I wanted ear covering headphones, which these are to block out some the noise. These headphones have a freq range of 4Hz to 24KHz so, they reach down to the depths and up to the highs. Worth a try IMO. Otherwse, there are plenty of HPs and EBs out there that'll work well with an iPod.
Anker makes a few pair of wireless headphones in the $30 range that all seem to have good reviews on Amazon. They probably aren't as convenient as the AirPods or BeatsX, though, since there is no W1 chip.