I'd take her to Walmart and have her look over the selection of sewing machines. She may like a computerized machine with some decorative stitches. Kids like to experiment with the decorative stitches.
I have several of the Brother mechanical machines; one is at my sisters in NJ; the other is used on the rare occasion that I take a sewing machine to a guild meeting. Both work well.
I also have two computerized Brother machines, the SQ9185 and the CE1100PRW. I think, but haven't measured so not certain, that the throats of these machines are a bit larger than the throats of the mechanicals. Bottom line, I am happy with them as well.
Thread balling up under the needle: When I begin to sew seems to be caused by positioning fabric such that they are in front of the needle (closer to you ), not under it. Moving the fabric so that the needle is 1/4" in from the edge of the fabrics (farther from you) seems to prevents that. But you probably already know that...
One feature to consider that most of us don't think about before we buy a sewing machine:
Brother sewing machine manuals are among the best that I have used. I used to write system requirements and user manuals/guides for billing systems, so I know a good one when I see one.