It's really discouraging to sew on a machine that may have a 'seizure' at any time. So I don't sew much. It's a fascinating article on differences between threads. To begin sewing I would not recommend a serger. A good basic sewing machine is best to begin with.
Sergers can be difficult to thread and the finished up seams are permanent.
As a beginner or, alas, even as an experienced sewer you and your daughters will find the need to unpick a seam or two and start over pretty often which you can do easily with sewing machine seams but which is almost impossible with serged seams. The Brother you have is a good brand. There are shops that specialize in reconditioning sewing machines. Sears Kenmore is a good basic inexpensive brand. Their new sewing machines are no more now than they were when I bought mine over 20 years ago.