Many machines have good records. Singer, New Home, Bernina, Brother, and more. What you need to look for for a machine for a beginner is basic things. Straight stitch. Zig Zag. Maybe a stretch stitch. Just basic stitches. From there she can go forward.
When she gets to a point where she is interesting in the next steps she may be old enough to do some chores and babysit to help buy a higher level machine.
For a beginner she doesn't need more than the basics. If you sew then a new machine could have a lot more. That way you can benefit from the machine too. If you don't sew perhaps you can learn alongside her and then both of you will have a new skill...
One of the best things I ever learned from is this.
Take the machine and get it all set up.
Put the needle in but don't thread it.
Take a piece of notebook paper and put it under the presser foot. Sew along the lines. Each and every line on the paper. Then get another one. Continue until both of you have a good feel for the machine, how much pressure you have to put on the foot pedal, how fast you like to sew, how to manage the back stitch, the different stitches, etc.....
The most important part of this activity is that you'll feel comfortable with the machine AND you'll be able to sew a straight stitch.
My mother in law and several other people have commented on how straight my seams are. I attribute that skill to this activity. I didn't sew on my machine for days. We all did this in beginning sewing in Jr. High. I think it made us much more comfortable with sewing and with managing the machine.
Good luck! If you need help picking patterns or come across a problem post another question!