I just found at a yard sale a little vintage Singer Merritt 1/2 size machine that has seperate settings for slow or fast, the foot pedal just makes it run. I got it for my granddaughter who is 7.
I have read good reviews of the Kenmore 3/4 machine made by janome. It has some zigzag stitches and priced under $100. (Same machine as the blue HELLO KITTY, but white plastic)
I think the machines made just for kids are usually not worth the money. Better to get a small real machine that will sew nicely and last.