I'm a professional musician, (you couldn't guess that from my name could you!) and I agree that the recorder is a good starting point, particularly for learning to read music. The piano can be difficult to learn before about age 6 or 7, largely because of hand size, and development of muscles in the fingers.
My thought is that if you are debating between a wind and string instrument, before about age 10, always go for the string - particularly the violin. It helps develop your ear for tuning, as you have to 'make' the note yourself whereas on a wind instrument it is largely down to the combination of keys. Before age 10 or 11 it is very hard for a child to learn a wind instrument (with the possible exception of the flute) because their lungs physically aren't big enough. Also, the wind instruments don't come in different sizes for little fingers as the string instruments do. Lastly, if your child wants to play in school orchestra or to go further, there are far more opportunities for violinists, as there are 20 or 30 violinists, compared to 2 or 3 clarinettists.
Some children can find piano hard, because of the independence of the two hands, and a melody instrument can be easier, but as aloha says, you can always find times to play the piano. (Piano is my instrument incidentally, and I'm not a string player in case you thought I was biased!).
So I would recommend, start off on recorder, or violin, and then if they want to do a wind instrument later, they've got a good musical grounding. (Lots of schools will lend you instruments, so it needn't be really expensive buying different instruments). I definitely want ds to start violin early on.