That's a 3rd gen iPod shuffle, so do not get the new Apple EarPod headphones. Based on posts I've read here, they do not work with the 3rd gen shuffle.
You can still find the old version of the Apple headphones with remote, at online stores like Amazon. They are like the one that came with your shuffle, except they usually have a microphone on the remote nub.
Alternately, you can use something like this adapter with remote controls
and connect ANY headphones.