Looking up the JWL-1221VS, the headstock has a spindle thread size of 1"x8. That's the number you want to look for when getting a chuck. My Rikon midi lathe has a 1"x8 thread, and I used a Nova G3 chuck on it. Some of the G3's are direct thread, meaning the chuck will only fit the specified thread, while others are inserts, where you buy an insert that matches the thread of your headstock. You can get a variety of different jaws that fit on the chuck for different size work.
Depending on where you are, pop into a local Woodcraft or Klingspor store, and they should be able to guide you to the right chuck and jaws you'll need. That Jet is a pretty common lathe, and will be easy to find a compatible chuck.