In my opinion a lesser expensive/cheap machine will always be a cheap machine, often frustrating in its need for constant adjustment and lack of stitch quality. Over the yeasrs I have encouraged many people to seriously look at a Bernina Record 807 or Record 830 machine (used, these were made in the 1970s) and they have been delighted they did so.
You can't hurt these machines! They are all solid metal (which means they are heavy!), made in Switzerland, have an extension table for larger sewing surface, can be easily maintained at home by a knowledgeable person, and have enough stitches to keep your grandaughter sewing for years into her adulthood. They are straight forward as to threading and changing the bobbin.
Right now there are several available on Ebay; search "Bernina Record 830 sewing machines" or the Record 807 - which has fewer stitches and is more basic than the 830. (Do not be confused by Bernina's NEW 830 which costs a much as a car!!)
She'll thank you for a long time if this is her first sewing machine!
Jan in VA