Guitar and percussion are best suited for 8 to 10-year-olds, or 7-year-olds who are physically ready. A good route for a younger child is to start with piano to build basic fundamentals, then allow them to choose drums or guitar when they get older. Guitar in particular calls for strong fingers (not teensy little ones!), and drummers need good arm strength. However, 5 and 6-year-olds can learn the ukulele before transitioning to the guitar.
10 years or preferably older has long been quoted as the appropriate age for private vocal lessons. Vocal chords have to be matured and ready, otherwise underdeveloped little chords are susceptible injuries caused by singing. In some cases, it might even be best to wait until puberty. Piano lessons happen to be a wonderful addition to vocal lessons, as singers can eventually learn to accompany themselves on the piano. They'll be ready for Open Mic Night in no time!