After having kids try nearly everything...two come to mind a flute. Flutes are relatively easy to play, portable and since they don't require a reed (like a clarinette) are dentist friendly. The other is an acoustic guitar. Similar thoughts and being acoustic are less likely to piss off the neighbors. Regardless of what you get...get quality. Cheap instruments do not have the quality of sound needed to keep the kid interested.
Do you mean a recorder? Recorder is not a popular instrument here in my area. I had short classes on how to play it when I was on junior high school, but nothing more. Guitars and violins have different sizes based on age and body size, so they cost more than common instruments.
Ultimately it depends on what the kids like to play. Parents are responsible to show them as many instruments as possible, I guess.