It is possible to find these instruments fairly cheap, but as you or your child progress you might want to shell out on a more professionally-designed instrument, which can be expensive.
Violin - an old favourite used to play classical and popular music styles;
Viola - classical, warmer sound than violin but more difficult to learn;
Cello - bulky and not particularly mobile, used in classical, jazz and some popular music;
Double Bass - even larger than Cello, musically versatile and used in many genres from classical to rock, and there are smaller sizes for children to learn. All of these appeal to sociable people who are eager to contribute to a group endeavour.