L.J.
Dear M.,
My daughter bought her first violin for $60 with case and bow brand new from The Violin Company. That was 2 years ago but they always have good sales. Personally, I would not go much more than that for her first violin since you don't know whether she will stick with it or not.
If she sticks with it, she will outgrow the violin, in her ability. Then you can think about a more expensive one. My daughter outgrew hers because she advanced so quickly since she had piano for 10 years. L. J