mom-6, Joe has made some excellent suggestions and here's my $0.02:
Look for:
1) All-metal.
2) Takes common parts such as bobbin and bobbin case, needles, etc.
3) Powerful motor, the higher the amperage the better. In my experience, 0.8 - 1.0 is good, 1.2 amps is better.
4) Easy to repair yourself.
5) Price.
6) Stitches. Depending upon what you're sewing, utility stitches are more important than decorative stitches. However, if this is your first zig-zag and you don't see yourself buying another (Sewing Machine Acquisition Disorder is highly contagious, fyi), try to find one with utility, stretch, and decorative stitching capability rather than a more limited machine.
7) Stitch width. Wider is better, as it gives you more options. Many domestic machines (meaning for home sewing) I've run are 4mm. Many Kenmores are 5mm. I have an industrial that goes to 8mm.
8) Shank height. Low shank feet and attachments are commonly found. High shank and super-high shank (a Kenmore proprietary design, I believe) are less commonly found but adapters can be purchased that will accept low shank attachments. Additionally, if you plan to sew materials that are bulky, try to find a machine whose presser foot can be raised well above the needle plate. When considering a machine, operate the presser foot lift and see how high the foot rises at the max height.
9) You'll probably be sewing straight-stitch on your zig-zag machine. Switching between the two should be easy and quick. Some machines have a small plate under the needle area that only has to be lifted and reversed (straight hole on one end, wide zig-zag hole on the other), negating the need to use a screwdriver and changing of the entire needle plate. It's a small consideration but a feature I really appreciate.
10) Built-in buttonhole capability.
Kenmore, White, Brother, Singer, and Japanese 'badged' or 'clone' zig-zag machines all can be found for very little money. Some are in great shape and only need cleaning and oiling, if that. Others need more serious attention.
Last edited by KenmoreRulesAll; 12-22-2014 at 09:56 AM.