I was just asked about what sewing machine a serious beginner should buy, for less than $250. It needs to be a good, durable sewing machine, that will grow with skill level.
To get a new machine that would be more durable, you’d need to spend at least $700. There are a lot of new machines that have lots of bells and whistles, but they all have a plastic bobbin case, that can cause a lot of frustration.
You might want to look on Craigslist.com, and see what used machines are available in your area. For new sewists, I recommend an old Kenmore 10 stitch, or something similar. I LOVE the old Kenmores! And you can usually find one in a thrift store for less than $25. Some only have straight and zig-zag stitches, with a door on top to add cams. You don’t want that, you want one with built-in cams/stitches. You also don’t want the old, top-loading Kenmores, as that bobbin/hook system is a nightmare. You want a front-loading machine with all metal hook and bobbin case, and a few extra stitches built-in.
If you've got your heart set on a "NEW" machine, Try a Singer "Simple." It has the metal oscillating hook and some nice stitches.
Most people only use a handful of stitches. The ones most people need are straight stitch, zig-zag, blind hem and serpentine (or broken zig-zag). If you’re a quilter, you need the blanket-stitch for applique. And a nice decorative stitch or two is good. If you’re sewing heavy fabrics, you need a front loading, metal hook and bobbin case. The plastic bobbin cases jam when you sew heavy fabric, and the needle goes right through them. Then you have to buy a new bobbin case. If you’re doing light sewing, like piecing a quilt, a cheap plastic machine will work just fine.
The auto thread cutters (under the needle plate) seem like a good idea, but they haven’t been perfected yet, and can cause a lot of grief.
To check the quality of a machine, grab the needle bar and try to wiggle it forward and backward. If it has forward/backward wiggle, the needle hook distance (a timing setting) is variable and you’re not likely to get as good stitch quality.