Plastic bobbins are fine. I don't suggest metal bobbins in plastic cases because they wear the case out.
Chances are good that your machine does need a bobbin case. It should be easy to get one, class 15 cases are among the most inexpensive and most plentiful ones around. The thing you need to figure out is which way the "finger" on the bobbin case goes - to the 11 o'clock position or the 1 o'clock position (probably 1 o'clock), and then get a case that is good for zig zag.
More than likely, it's the one shown on this page:
http://www.sewingpartsonline.com/ken...ine-parts.aspx
That's probably not the best price but a great site for figuring out what stuff looks like.